Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#2368 |
| 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 | |
548 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)(18,19,21,20)(22,23)(24,27)(25,26)(28,29)(30,31,34,35)(32,36,37,33);(18,20,21,19)(23,26)(27,29)(31,35)(33,36);(22,24,25,28)(23,27,26,29)(30,32)(31,33)(34,37)(35,36);(22,23)(24,27)(25,26)(28,29)(30,33)(31,32)(34,36)(35,37)850 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1100);