Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of #7540 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#7541 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1415 |
| commutator | C32 | C2×C4×C17 |
| Frattini, cosocle | C2×C32 | C22×C17 |
| prime radical | C2×C17×D32 | C2 |
| 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 | |
94 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)(18,19,21,28,25,31,24,49)(20,32,35,59,39,26,38,50)(22,42,40,75,46,55,45,77)(23,47,41,63,48,78,44,30)(27,53,56,33,58,66,79,36)(29,61,60,34,54,69,76,43)(37,72,67,52,74,62,70,65)(51,80,57,71,64,73,81,68);(19,26)(20,33)(21,24)(22,43)(23,44)(27,54)(28,59)(29,58)(30,62)(31,32)(34,46)(35,53)(36,39)(37,73)(38,66)(40,69)(41,48)(42,51)(45,61)(47,52)(49,50)(55,64)(56,60)(57,77)(63,72)(65,78)(67,71)(68,70)(74,80)(75,81)(76,79)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 529);