Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8490 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#538 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,38,45,68,71)(14,24,27,53,26,59,36,67)(15,30,33,62,32,48,64,73)(17,20,37,44,18,23,39,51)(19,40,43,25,55,57,50,56)(21,46,49,35,52,66,75,34)(28,54,60,74,29,47,61,72)(31,41,63,69,58,42,65,70);(12,14,17,28)(13,19,20,41)(15,31,34,56)(16,36,37,61)(18,29,38,26)(21,47,30,59)(22,50,44,70)(23,42,45,55)(24,52,54,48)(25,32,58,35)(27,39,60,68)(33,65,46,57)(40,64,63,66)(43,51,69,71)(49,74,62,53)(67,75,72,73);(13,20)(15,32)(16,37)(19,41)(21,48)(23,45)(24,47)(25,56)(27,60)(30,52)(31,58)(33,66)(34,35)(36,61)(39,68)(40,65)(42,55)(46,64)(49,75)(53,67)(54,59)(57,63)(62,73)(72,74)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1478);