Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×#2862 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
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)(19,20)(22,23,26,29)(24,27,28,25)(32,36)(34,37);(18,19,21,20)(22,24,26,28)(23,27,29,25)(30,31,33,35)(32,34,36,37);(22,25,26,27)(23,28,29,24);(18,20,21,19)(22,23)(24,27)(25,28)(26,29)(30,32)(31,34)(33,36)(35,37)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1594);