Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C11×#1923 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C24×C11 | C22×C4 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
1462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4)(5,6)(8,9)(11,12,14,17,15,13,16,18);(7,8,10,9)(11,13,14,18,15,12,16,17);(4,6)(7,9,10,8)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14032);