Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×C8×Q8×C11 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8×C11 | C22 |
| commutator | C2 | C22×C4×C8×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle, prime radical | C23×C11 | C23×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8×C11 ◁ G | |
1070 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31);(5,6,7,8,9,10,11,12);(13,14,15,16)(17,20,19,18);(13,17,15,19)(14,18,16,20)1760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13503);