Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C210 |
| direct product | C23×D8×C17 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | D4 |
| commutator, Frattini, cosocle | C4 | C25×C17 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ C23×C4×C17 ◁ G | |
1976 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6);(7,8,9,10,11,12,13,14);(8,14)(9,13)(10,12)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2306);