Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1426 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #367 |
| commutator | C16 | C2×C4×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| prime radical | C22×C17 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ G | |
52 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)(19,24,26,37)(20,29)(21,33)(22,34)(25,40)(27,41,44,49)(28,47,45,39)(30,35)(31,43)(32,42)(36,48,46,38);(18,19,25,41,21,27,20,24,34,45,29,38,30,36,40,47,23,26,43,49,35,44,32,37,22,28,42,48,33,46,31,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 158);