Finite Group DatabasebetaFinite Group Databasebeta| order | 30894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C271 ⋊ C2×C3 |
| Hall | #29508952 ⋊ C2 |
| Hall | D5149 ⋊ C3 |
| Sylow | C271 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ D271⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C271 | C2×C3 |
| LCS | G ▷ C19×C271 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 290 |
| transitive degree | μt(G) = 5149 |
A minimal faithful permutation representation — 2 generators on 290 points:
(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(21,25,26,22,23,27)(24,33,34,28,29,43)(30,46,47,36,37,60)(31,45,41,39,35,32)(38,65,66,49,50,83)(40,63,64,52,48,57)(42,44,62,54,55,58)(51,88,89,68,69,112)(53,86,87,71,67,80)(56,61,85,73,74,81)(59,101,99,77,78,76)(70,117,118,91,92,147)(72,115,116,94,90,109)(75,84,114,96,97,110)(79,130,131,102,103,105)(82,136,128,106,107,100)(93,152,153,120,121,188)(95,150,151,123,119,144)(98,113,149,125,126,145)(104,165,166,132,133,140)(108,172,170,137,138,135)(111,177,163,141,142,129)(122,193,194,155,156,234)(124,191,192,158,154,185)(127,148,190,160,161,186)(134,205,206,167,168,181)(139,212,213,173,174,176)(143,218,210,178,179,171)(146,223,203,182,183,164)(157,239,240,196,197,275)(159,237,238,198,195,231)(162,189,236,200,201,232)(169,247,248,207,208,227)(175,254,255,214,215,222)(180,261,259,219,220,217)(184,266,252,224,225,211)(187,269,245,228,229,204)(199,277,278,242,241,273)(202,235,276,244,243,274)(209,280,281,249,250,271)(216,284,285,256,257,268)(221,288,289,262,263,265)(226,290,287,264,267,260)(230,286,283,258,270,253)(233,282,279,251,272,246);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(20,21,24,30,38,51,70,93,122,157,197,241,250,257,263,267,270,272,274,275,244,200,160,125,96,73,54,41,26,25,31,40,53,72,95,124,159,199,243,156,195,208,215,220,225,229,232,234,273,279,245,203,163,128,99,64,34,45,33,44,59,79,104,134,169,209,251,201,121,154,168,174,179,183,186,188,231,271,283,252,210,170,131,87,47,62,63,46,61,82,108,139,175,216,258,228,161,92,119,133,138,142,145,147,185,227,268,287,259,213,166,116,66,85,101,86,65,84,111,143,180,221,264,224,182,126,69,90,103,107,110,112,144,181,222,265,289,255,206,151,89,114,136,130,115,88,113,146,184,226,262,219,178,141,97,50,67,78,81,83,109,140,176,217,260,285,248,192,118,149,177,172,165,150,117,148,187,230,256,214,173,137,106,74,37,48,58,60,80,105,135,171,211,253,281,238,153,190,223,218,212,205,191,152,189,233,249,207,167,132,102,77,55,29,35,43,57,76,100,129,164,204,246,278,194,236,269,266,261,254,247,237,193,235,242,198,158,123,94,71,52,39,23,27,32,42,56,75,98,127,162,202,240,276,282,286,290,288,284,280,277,239,196,155,120,91,68,49,36,28,22)Polycyclic presentation:
2,3,19,271|c^a=c^18,d^a=d^270,c^b=c^7,d^b=d^242864 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30894, 23);