Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | Q8×C11×#103 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G | |
1086 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)(5,8,7,6)(21,22,23,24,25,26,27,28,29,30,31);(1,5,3,7)(2,6,4,8);(9,10,11,12)(14,17)(15,19)(18,20);(13,14,16,18)(15,20,19,17)770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15508);