Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13369 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
378 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(26,27,29,34)(28,38,40,32)(30,33,43,49)(31,36,44,37)(35,51,50,45)(39,47,42,52)(41,56,55,48)(46,54,53,57);(18,20,21,25)(19,22,23,24)(26,28,29,40)(27,32,34,38)(30,41,43,55)(31,39,44,42)(33,48,49,56)(35,46,50,53)(36,52,37,47)(45,54,51,57);(27,33)(28,39)(30,45)(31,44)(32,46)(34,49)(35,37)(36,50)(38,53)(40,42)(41,55)(43,51)(47,56)(48,52)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6357);