Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#7729 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C43×C17 ◁ G | |
346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,23)(21,29)(22,25)(24,30)(27,31,33,32)(34,35)(36,42,44,49)(37,41)(38,40)(39,43,47,45)(46,48)(50,51,53,57,54,56,62,64)(52,58,60,65,59,55,61,63);(18,20)(19,23)(21,27)(22,28)(24,31)(25,26)(29,32)(30,33)(34,36,38,44)(35,39,40,47)(37,45,46,43)(41,49,48,42)(50,52)(51,55)(53,61)(54,59)(56,58)(57,65)(60,62)(63,64);(18,21,22,30)(19,24,25,29)(20,27,28,33)(23,31,26,32)(35,40)(39,47)(41,48)(42,49)(51,56)(52,59)(57,64)(60,61)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 717);