Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C17×#418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×D4 |
| commutator | C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C23×D4×C17 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 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)(9,13)(10,12)(11,14);(8,12)(9,10)(13,14);(7,9,11,10)(8,13,14,12)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1625);