Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#2821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C24×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,25,27)(24,26,28,29)(31,35)(36,38)(37,41)(44,45);(19,21)(24,28)(26,29)(30,31)(32,38)(33,41)(34,35)(36,40)(37,43)(39,44)(42,45);(18,19)(20,21)(22,23)(24,26)(25,27)(28,29)(30,32,34,40)(31,36,35,38)(33,42,43,39)(37,45,41,44);(22,24)(23,26)(25,28)(27,29)(30,33,34,43)(31,37,35,41)(32,39,40,42)(36,44,38,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1553);