Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60876 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35,40,44)(36,41,47,56)(37,49,51,57)(38,43,39,52)(42,53,58,50)(45,59,61,64)(46,55,48,62)(54,63,65,60);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,41)(37,45)(38,46)(39,48)(40,47)(42,54)(43,55)(44,56)(49,59)(50,60)(51,61)(52,62)(53,63)(57,64)(58,65);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,37)(35,42)(36,45)(38,50)(39,53)(40,51)(41,54)(43,57)(44,58)(46,60)(47,61)(48,63)(49,52)(55,64)(56,65)(59,62);(19,25)(23,26)(24,33)(31,32)(34,38,40,39)(35,43,44,52)(36,46,47,48)(37,50,51,53)(41,55,56,62)(42,57,58,49)(45,60,61,63)(54,64,65,59);(36,47)(41,56)(45,61)(46,48)(54,65)(55,62)(59,64)(60,63)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53864);