Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#2564 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
584 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)(19,21)(22,23,26,27)(24,25,28,29)(31,32)(33,37);(23,27)(24,28)(30,31,34,32)(33,35,37,36);(18,19,20,21)(22,24)(23,25)(26,28)(27,29)(30,32,34,31)(33,36,37,35);(22,25)(23,24)(26,29)(27,28)(30,33)(31,35)(32,36)(34,37)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1296);