Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17410 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×Q8×C17 ◁ G | |
848 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,25,22,24,28,31)(20,23,27,30,26,29,32,33)(34,35)(36,44,47,40)(37,41)(38,42)(39,43)(45,58,61,52)(46,59,63,53)(48,54)(49,55)(50,56)(51,57)(60,65,62,64);(18,20)(19,23)(21,27)(22,26)(24,29)(25,30)(28,32)(31,33)(34,36,39,47)(35,40,43,44)(37,45,49,61)(38,46,51,63)(41,52,55,58)(42,53,57,59)(48,60,50,62)(54,64,56,65);(20,26)(23,29)(27,32)(30,33)(34,37,39,49)(35,41,43,55)(36,45,47,61)(38,50,51,48)(40,52,44,58)(42,56,57,54)(46,62,63,60)(53,65,59,64);(19,24)(23,29)(25,31)(30,33)(34,38,39,51)(35,42,43,57)(36,46,47,63)(37,48,49,50)(40,53,44,59)(41,54,55,56)(45,60,61,62)(52,64,58,65)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10398);