Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#2949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator | C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#117 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 544 |
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)(18,19,21,20)(22,23)(24,30)(25,33)(26,28)(27,31)(29,35)(32,37)(34,36);(22,24,26,32)(23,27,28,36)(25,34,35,31)(29,37,33,30);(18,20,21,19)(22,23)(24,27)(25,29)(26,28)(30,31)(32,36)(33,35)(34,37);(23,28)(27,36)(29,33)(30,37)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1681);