Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#2398 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| socle | C23×C17 | C24 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
568 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)(22,23,26,28)(24,29,25,27)(30,31,33,35)(32,36,37,34);(18,19)(20,21)(22,24,26,25)(23,27,28,29)(30,32,33,37)(31,34,35,36);(19,21)(31,35)(34,36);(22,25,26,24)(23,27,28,29)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1130);