Finite Group DatabasebetaFinite Group Databasebeta| order | 13255 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C241 ⋊ C5 |
| Sylow | C241 ⋊ C11⋊C5 |
| Sylow | C11 ⋊ C241⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C241 | C5 |
| LCS | G ▷ C11×C241 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 252 |
| transitive degree | μt(G) = 2651 |
A minimal faithful permutation representation — 2 generators on 252 points:
(2,3,5,9,17)(4,7,13,25,47)(6,11,21,40,33)(8,15,29,45,82)(10,19,36,18,34)(12,23,44,80,86)(14,27,51,93,62)(16,31,58,103,163)(20,38,69,48,87)(22,42,76,73,63)(24,46,84,137,134)(26,49,89,35,64)(28,53,97,156,141)(30,56,98,157,110)(32,60,107,168,215)(37,67,41,74,66)(39,71,119,83,135)(43,78,129,131,142)(50,91,146,88,72)(52,95,152,122,111)(54,99,159,202,190)(55,85,139,65,112)(57,101,161,211,196)(59,105,165,79,130)(61,94,150,114,70)(68,116,81,132,143)(75,124,118,90,144)(77,127,126,123,115)(92,148,200,136,191)(96,154,205,186,121)(100,160,209,178,170)(102,162,212,236,228)(104,164,108,113,171)(106,167,214,184,223)(109,153,203,182,179)(117,174,138,192,193)(120,177,158,207,173)(125,180,176,140,194)(128,183,185,187,197)(133,188,198,145,149)(147,199,151,181,175)(155,206,217,166,213)(169,216,237,172,218)(189,226,231,195,229)(201,232,208,233,219)(204,227,224,225,230)(210,234,222,221,220)(235,241,238,239,240)(243,244,246,249,252)(245,248,247,250,251);(1,2,4,8,16,32,61,109,107,169,129,185,224,238,241,87,142,119,176,93,15,30,57,102,38,70,89,143,49,90,145,23,45,83,136,42,77,128,184,51,94,151,27,52,96,155,44,81,133,189,227,34,63,29,55,40,73,122,178,206,216,215,36,66,114,173,191,213,232,240,207,171,217,162,211,180,221,194,214,188,225,209,174,192,167,212,183,3,6,12,24,9,18,35,65,113,172,163,5,10,20,39,72,121,177,220,150,31,59,106,156,71,120,144,197,91,147,152,46,85,140,195,78,103,146,198,95,153,204,53,98,158,208,82,134,190,228,97,64,111,56,100,74,123,84,138,80,131,186,67,115,58,104,76,126,182,222,233,218,237,69,118,175,219,229,236,226,239,234,47,86,141,196,223,7,14,28,54,19,37,68,117,25,48,88,11,22,43,79,21,41,75,125,181,60,108,13,26,50,92,149,202,148,201,203,17,33,62,110,130,164,199,230,154,168,205,99,160,210,235,135,165,200,231,157,112,170,101,161,124,179,139,193,132,187,159,116,137,105,166,127)(242,243,245,246,249,244,247,251,250,252,248)Polycyclic presentation:
5,11,241|b^a=b^5,c^a=c^87535 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#27210423, #40997194, #40997200, … |
| maximal normal subgroup of | C2×#27210423, #40997194, #40997200, … |
| maximal quotient of | C2×#27210423 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13255, 5);