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×#2176 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | C2×D8 |
| commutator | C8 | C22×C4×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ G | |
148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,32)(25,36)(26,41)(27,29)(28,33)(30,39)(31,38)(34,52)(35,49)(37,47)(40,48)(42,46)(43,51)(44,53)(45,50);(22,24,27,35)(23,28,29,43)(25,37,40,53)(26,42,38,34)(30,46,45,52)(31,47,41,44)(32,48,49,36)(33,50,51,39);(18,20,21,19)(23,29)(28,43)(30,45)(31,41)(32,49)(36,48)(44,47)(46,52)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 908);