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×#2967 |
| 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×#121 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
362 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)(20,23)(21,22)(24,25)(26,27,29,33,30,32,36,39)(28,31,35,38,34,37,40,41);(19,22)(23,25)(28,34)(31,37)(35,40)(38,41);(26,28,29,35,30,34,36,40)(27,31,33,38,32,37,39,41);(18,20,21,24)(19,23,22,25)(27,32)(31,37)(33,39)(38,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1699);