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×#1419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #357 |
| commutator | C16 | C2×C4×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| prime radical | C2×C17×D16 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ G | |
78 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)(18,19,21,27,24,29,23,40)(20,30,33,47,36,25,35,41)(22,37,32,44,39,45,38,28)(26,43,42,31,46,49,48,34);(19,25)(20,31)(21,23)(22,38)(26,44)(27,47)(28,46)(29,30)(32,39)(33,43)(34,36)(35,49)(37,42)(40,41)(45,48)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 151);