Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21)(22,32)(23,31)(24,27)(25,38)(26,29)(28,35)(30,40)(33,49)(34,48)(36,43)(37,45)(39,47)(41,46)(42,50)(44,51);(12,14,15,19)(13,16,17,18)(21,27)(28,42)(29,31)(30,43)(32,48)(38,45)(44,47)(46,49);(14,19)(16,18)(20,22)(21,28)(23,33)(24,34)(25,39)(26,41)(27,42)(29,44)(30,46)(31,47)(32,38)(35,40)(36,50)(37,51)(43,49)(45,48);(13,17)(16,18)(20,23,24,26)(21,29,27,31)(22,33,34,41)(25,36,37,40)(28,44,42,47)(30,45,43,38)(32,46,48,49)(35,39,50,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26773);