Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C17×#494 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(4,6)(7,8,11,14)(9,15,18,22)(10,19,16,13)(12,20,21,17);(7,9,16,20,11,18,10,17)(8,12,19,22,14,21,13,15);(3,4,5,6)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1877);