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×#1420 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #357 |
| commutator | C16 | C2×C4×C17 |
| Frattini, cosocle | C2×C16 | C22×C17 |
| prime radical | C22×C17 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ G | |
70 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)(18,19,22,28,25,30,24,48)(20,31,33,62,36,64,35,71)(21,37,40,72,43,74,42,79)(23,44,39,60,47,55,46,29)(26,49,50,32,52,66,58,68)(27,53,56,78,57,77,73,41)(34,69,65,54,70,81,45,63)(38,59,75,80,67,61,76,51);(18,20,25,36)(19,26,30,52)(21,38,43,67)(22,35,24,33)(23,45,47,65)(27,54,57,63)(28,58,48,50)(29,59,60,61)(31,37,64,74)(32,41,68,78)(34,39,70,46)(40,76,42,75)(44,51,55,80)(49,53,66,77)(56,69,73,81)(62,79,71,72)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 152);