Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7548 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7548 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1424 |
| commutator | C32 | C2×C4×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| prime radical | C22×C17 | SD64 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C8×C17 ◁ C2×C16×C17 ◁ C2×C17×C32 ◁ G | |
62 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)(19,25,27,43)(20,31)(21,36)(22,37)(23,40)(26,47)(28,56,53,70)(29,60,54,80)(30,61,55,46)(32,39)(33,50)(34,52)(35,51)(38,65)(41,68)(42,69,58,44)(45,73,72,57)(48,75,76,71)(49,78)(59,81,79,77)(62,63)(64,74)(66,67);(18,19,26,48,21,28,49,72,37,57,64,70,67,75,35,43,23,30,51,69,38,59,74,80,41,54,78,81,32,42,47,61,24,27,52,76,39,53,33,45,68,73,63,56,65,71,20,25,40,55,31,44,66,79,62,60,22,29,50,77,36,58,34,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 536);