Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33778 |
| 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 | |
598 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)(33,48)(34,50)(36,43)(37,45)(39,47)(41,46)(42,49)(44,51);(12,14,15,19)(13,16,17,18)(21,27)(22,33)(29,31)(30,43)(34,41)(35,49)(38,45)(39,51);(14,19)(16,18)(20,22)(21,28)(23,34)(24,33)(25,39)(26,41)(27,42)(29,44)(30,46)(31,47)(32,38)(35,40)(36,49)(37,51)(43,50)(45,48);(13,17)(16,18)(20,23,24,26)(21,29,27,31)(22,34,33,41)(25,36,37,40)(28,44,42,47)(30,45,43,38)(32,46,48,50)(35,39,49,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26766);