Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60770 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×#41×C17 ◁ G | |
2132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27,31,35)(28,36,39,49)(29,33,40,47)(30,42,44,34)(32,43,46,38)(37,50,51,57)(41,54,53,48)(45,55,56,52);(18,20)(19,22)(21,25)(23,24);(20,25)(22,24)(26,28,31,39)(27,32,35,46)(29,37,40,51)(30,43,44,38)(33,45,47,56)(34,49,42,36)(41,55,53,52)(48,57,54,50);(19,23)(22,24)(26,29)(27,33)(28,37)(30,41)(31,40)(32,45)(34,48)(35,47)(36,50)(38,52)(39,51)(42,54)(43,55)(44,53)(46,56)(49,57);(29,40)(33,47)(37,51)(41,53)(45,56)(48,54)(50,57)(52,55)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53758);