Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#3455 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| socle | C22×C17 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
1040 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22)(21,23)(24,25)(26,27)(28,34)(29,33)(30,32)(31,35)(36,40)(37,39)(38,41);(18,20,21,24)(19,22,23,25)(26,28)(27,31)(29,36)(30,35)(32,34)(33,38)(37,41)(39,40);(19,23)(22,25)(28,35)(31,34)(36,41)(38,40);(27,32)(31,34)(33,39)(38,40);(26,29,30,37)(27,33,32,39)(28,36,35,41)(31,38,34,40)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2187);