Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61057 |
| 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 ◁ C17×#525 ◁ G | |
2696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,28,33)(24,34,37,48)(25,30,40,47)(26,32,27,31)(29,41,44,36)(35,50,52,45)(38,53,51,43)(39,49,42,46);(22,24,28,37)(23,29,33,44)(25,38,40,51)(26,36,27,41)(30,45,47,50)(31,34,32,48)(35,42,52,39)(43,49,53,46);(19,21);(22,25)(23,30)(24,35)(26,39)(27,42)(28,40)(29,43)(31,46)(32,49)(33,47)(34,50)(36,51)(37,52)(38,41)(44,53)(45,48);(22,26,28,27)(23,31,33,32)(24,36,37,41)(25,39,40,42)(29,34,44,48)(30,46,47,49)(35,51,52,38)(43,50,53,45)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54045);