Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42×C11 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×C11×#2875 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C2 | C23×C42×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
3278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33);(7,8,10,14,11,12,17,19)(9,13,16,20,15,18,21,22);(3,4,5,6)(8,12)(13,18)(14,19)(20,22);(7,9)(8,13)(10,16)(11,15)(12,18)(14,20)(17,21)(19,22);(9,15)(13,18)(16,21)(20,22)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53044);