Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#33326 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C2 | C22×C4×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,19,24,20,25,29,37,21,22,30,33,31,34,41,44)(18,23,27,35,28,36,40,45,26,32,38,42,39,43,46,47);(12,13,14,15)(17,22)(23,32)(24,33)(25,34)(35,42)(36,43)(37,44)(45,47);(16,18)(17,23)(19,27)(20,28)(21,26)(22,32)(24,35)(25,36)(29,40)(30,38)(31,39)(33,42)(34,43)(37,45)(41,46)(44,47);(18,26)(23,32)(27,38)(28,39)(35,42)(36,43)(40,46)(45,47)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26314);