Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1418 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #357 |
| commutator | C16 | C2×C4×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| prime radical | C17×#508 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ G | |
74 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)(19,24,25,40)(20,28)(21,33)(22,35)(26,44,43,48)(27,45,37,42)(29,34,41,39)(30,36)(31,49)(32,38)(46,47);(18,19)(20,29)(21,34)(22,37)(23,25)(24,38)(26,33)(27,35)(28,40)(30,43)(31,44)(32,41)(36,39)(42,47)(45,49)(46,48)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 150);