Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #2263 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C23×C17 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ G | |
112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,33)(22,36)(23,25)(26,29)(27,30)(28,34)(31,43)(32,37)(35,49)(38,45)(39,44)(40,46)(41,47)(42,48);(19,24)(20,29)(21,30)(22,34)(25,37)(26,27)(28,43)(31,48)(32,46)(33,38)(35,47)(36,39)(40,41)(42,49)(44,45);(19,25)(24,37)(26,40)(27,41)(28,36)(33,49)(38,42)(39,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 995);