Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#3156 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C2×C17×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#117 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23,27,31)(24,32,36,46)(25,29,37,43)(26,39,33,30)(28,40,42,35)(34,45,48,53)(38,50,47,44)(41,51,52,49);(22,24,33,40,27,36,26,35)(23,28,39,46,31,42,30,32)(25,34,47,51,37,48,38,49)(29,41,50,53,43,52,44,45);(18,19,20,21)(22,25)(23,29)(24,34)(26,38)(27,37)(28,41)(30,44)(31,43)(32,45)(33,47)(35,49)(36,48)(39,50)(40,51)(42,52)(46,53);(25,37)(29,43)(34,48)(38,47)(41,52)(44,50)(45,53)(49,51)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1888);