Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1357 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1358 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #331 |
| commutator | C42 | C2×C4×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| prime radical | C22×C17 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C4×C8×C17 ◁ G | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,22,25,34,41,23,28,35,44,37,27,45,43)(20,29,30,46,31,40,47,49,32,39,48,42,36,24,33,38);(18,20,23,32)(19,24,28,40)(21,33,35,47)(22,36,37,31)(25,39,27,29)(26,42,44,46)(30,34,48,45)(38,41,49,43)391 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 90);