Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#24989 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,19,25)(14,26,31,44)(15,32,36,51)(16,37,40,49)(17,24,18,23)(20,30,45,29)(21,41,48,35)(22,39,50,38)(27,46,33,42)(28,56,59,43)(34,64,66,47)(52,60,61,55)(53,58,69,57)(54,73,63,72)(62,67,71,65)(68,74,70,75);(12,14,18,30,19,31,17,29)(13,20,24,44,25,45,23,26)(15,33,35,60,36,27,41,55)(16,28,39,58,40,59,38,57)(21,46,32,61,48,42,51,52)(22,43,49,69,50,56,37,53)(34,63,65,75,66,54,67,74)(47,70,62,73,64,68,71,72);(12,15)(13,21)(14,27)(16,34)(17,35)(18,41)(19,36)(20,42)(22,47)(23,32)(24,51)(25,48)(26,52)(28,54)(29,55)(30,60)(31,33)(37,62)(38,65)(39,67)(40,66)(43,68)(44,61)(45,46)(49,71)(50,64)(53,72)(56,70)(57,74)(58,75)(59,63)(69,73);(12,16,18,39,19,40,17,38)(13,22,24,49,25,50,23,37)(14,28,30,58,31,59,29,57)(15,34,41,67,36,66,35,65)(20,43,44,69,45,56,26,53)(21,47,51,71,48,64,32,62)(27,54,60,75,33,63,55,74)(42,68,61,73,46,70,52,72)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17977);