Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2179 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×D8 |
| commutator | C8 | C22×C4×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C2×C17 | C4×D8 |
| prime radical | C17×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C8×C17 ◁ C4×C8×C17 ◁ G | |
144 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28,24,30,40,29)(20,31,33,46,35,48,34,42)(21,27,36,45,37,26,22,38)(25,41,43,49,44,39,47,32);(18,20)(19,25)(21,32)(22,39)(23,33)(24,35)(26,42)(27,46)(28,43)(29,47)(30,44)(31,38)(34,40)(36,41)(37,49)(45,48);(18,21,23,36,24,37,40,22)(19,26,28,38,30,27,29,45)(20,32,33,41,35,49,34,39)(25,42,43,31,44,46,47,48)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 911);