Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1365 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #102 |
| commutator | C2×C8 | C2×C4×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,24)(23,25)(26,27,29,32,31,35,28,36,30,34,37,40,38,41,39,33);(18,19,21,23)(20,25,24,22)(27,32)(28,37)(29,39)(31,38)(33,35)(34,40)(36,41)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 97);