Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61186 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3486 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#525 ◁ G | |
2022 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)(18,19,21,23)(20,24,25,22)(26,27)(28,36)(29,40)(30,34)(31,44)(32,38)(33,42)(35,43)(37,52)(39,47)(41,49)(45,48)(46,56)(50,54)(51,55)(53,57);(18,20)(19,22)(21,25)(23,24)(26,28)(27,32)(29,37)(30,38)(31,39)(33,46)(34,36)(35,47)(40,57)(41,53)(42,54)(43,55)(44,51)(45,56)(48,50)(49,52);(26,29,30,41)(27,33,34,48)(28,37,38,53)(31,45,43,42)(32,46,36,50)(35,49,44,40)(39,56,55,54)(47,52,51,57);(20,25)(22,24)(28,38)(32,36)(37,53)(39,55)(46,50)(47,51)(52,57)(54,56);(27,34)(28,38)(33,48)(35,44)(37,53)(39,55)(40,49)(54,56)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54174);