Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#2378 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator | C22 | C23×C4×C17 |
| Frattini, cosocle | C23 | C24×C17 |
| prime radical | C24×C17 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(23,26)(24,28)(30,31)(32,36)(33,35)(34,37);(23,26)(27,29)(30,31,33,35)(32,36,37,34);(22,23)(24,27)(25,26)(28,29)(30,31)(32,34)(33,35)(36,37);(22,24)(23,27)(25,28)(26,29)(30,32,33,37)(31,34,35,36)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1110);