Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C17 | D4 |
| commutator | C4 | C2×C16×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| socle | C2×C17 | C22⋊C16 |
| prime radical | #41×C17 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C17 ◁ C2×C16×C17 ◁ G | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,23,29,41,54,24,30,42,55,44,57,69,77,25,31,43,56,45,58,70,78,21,27,38,51,39,52,66,75)(20,32,34,59,35,60,63,79,33,49,61,53,62,73,80,76,36,50,40,67,64,74,68,81,37,26,46,47,65,48,71,72);(18,20)(19,26)(21,37)(22,40)(23,35)(24,33)(25,36)(27,50)(28,53)(29,48)(30,32)(31,49)(34,43)(38,61)(39,65)(41,68)(42,46)(44,62)(45,64)(47,56)(51,59)(52,74)(54,76)(55,67)(57,60)(58,73)(63,70)(66,80)(69,71)(72,78)(75,79)(77,81)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 133);