Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(D271⋊C5)) |
| unambiguous semidirect product | (C271⋊C5)⋊(C3⋊D3) |
| unambiguous semidirect product | (C3⋊D813)⋊C5 |
| Fitting, socle, derived, Hall | C32×C271 ⋊ C2×C5 |
| Hall | C32×C271⋊C5 ⋊ C2 |
| Hall | C3⋊D813 ⋊ C5 |
| Hall | C271⋊C5 ⋊ C3⋊D3 |
| Sylow | C271 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ D271⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C271 | C2×C5 |
| LCS | G ▷ C32×C271 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 277 |
| transitive degree | μt(G) = 2439 |
A minimal faithful permutation representation — 3 generators on 277 points:
(2,6,7,25,30,3,4,12,14,54)(5,19,20,86,91,9,10,41,43,158)(8,35,36,37,65,16,17,74,76,78)(11,48,49,42,134,22,23,102,88,89)(13,59,60,202,181,27,28,121,123,112)(15,69,70,66,67,32,33,71,31,77)(18,80,81,210,160,38,39,145,147,236)(21,96,97,250,132,45,46,169,171,213)(24,106,107,217,141,51,52,187,188,220)(26,116,117,55,192,56,57,195,113,114)(29,128,40,152,153,62,63,83,84,231)(34,137,58,161,162,72,73,119,92,238)(44,164,165,133,64,93,94,243,68,130)(47,176,105,261,237,99,100,184,185,260)(50,182,183,224,214,103,104,146,242,180)(53,177,191,229,230,109,110,190,151,270)(61,208,209,79,222,125,126,239,143,144)(75,111,98,256,257,140,131,173,174,193)(82,228,197,198,139,149,150,118,252,157)(85,154,234,205,221,155,156,232,235,267)(87,216,226,115,207,136,159,148,124,194)(90,204,200,166,206,142,122,120,244,245)(95,247,248,240,241,167,168,271,163,263)(101,108,233,264,129,178,179,189,269,211)(127,253,254,215,138,203,172,196,135,218)(170,212,262,258,259,219,251,186,175,265)(199,249,246,255,227,201,266,223,268,225)(273,274)(276,277);(1,2,5,11,24,53,111,130,62,27,4,8,18,40,85,157,36,77,142,88,10,21,47,101,180,213,78,54,112,49,23,50,105,186,263,264,144,114,193,104,52,108,190,209,238,234,165,194,265,185,110,176,260,236,158,231,245,202,256,258,173,96,170,218,137,217,268,253,169,167,93,41,87,70,69,135,147,208,251,211,128,89,133,66,25,55,115,121,203,125,59,122,205,216,57,118,199,200,119,56,7,15,34,43,92,163,242,267,220,140,17,37,79,94,166,246,81,148,227,183,39,82,151,168,249,271,150,117,196,107,84,154,233,171,252,270,230,198,250,189,156,152,187,254,195,228,248,266,247,229,149,80,146,225,226,145,223,244,164,143,76,35,75,141,221,224,240,161,86,72,32,12,26,58,120,201,197,116,159,235,204,28,61,127,60,124,113,14,31,68,134,63,129,212,126,210,215,33,71,136,20,44,95,97,172,255,188,73,138,219,46,98,175,174,123,206,153,91,160,237,100,177,261,259,207,243,232,162,239,191,179,106,182,257,192,222,269,241,262,184,103,48,102,181,30,65,132,214,178,99,45,19,42,90,67,74,139,155,83,38,16,6,13,29,64,131,109,51,22,9,3)(275,276,277);(272,273,274)Polycyclic presentation:
2,5,3^2,271|c^a=c^2,d^a=d^2,e^a=e^270,e^b=e^10273 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 32);