Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#2981 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C24 |
| commutator | C22 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C23×C4 |
| prime radical | C17×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27,30,34,29,33,37,41)(28,32,36,40,35,31,38,39);(18,20)(19,22)(21,25)(23,24)(26,28)(27,31)(29,35)(30,36)(32,33)(34,39)(37,38)(40,41);(20,25)(22,24)(26,28)(27,32)(29,35)(30,36)(31,33)(34,40)(37,38)(39,41);(19,23)(22,24)(27,33)(28,35)(34,41)(36,38)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1713);