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×#2264 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C23×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 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,30)(21,35)(22,41)(23,45)(24,26)(25,31)(27,38)(28,37)(29,43)(32,62)(33,65)(34,57)(36,54)(39,73)(40,56)(42,52)(44,75)(46,58)(47,61)(48,69)(49,68)(50,59)(51,63)(53,80)(55,60)(64,81)(66,71)(67,72)(70,79)(74,77)(76,78);(18,20,24,34)(19,25,26,47)(21,36,40,70)(22,42,44,76)(23,46,43,33)(27,52,50,78)(28,54,51,79)(29,55,45,49)(30,56,57,35)(31,59,61,38)(32,63,64,37)(39,74,72,69)(41,48,75,77)(53,81,66,62)(58,67,65,73)(60,71,68,80);(19,26)(25,47)(27,50)(28,51)(29,45)(30,57)(35,56)(41,75)(48,77)(49,55)(52,78)(53,66)(54,79)(58,65)(62,81)(67,73)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 996);