Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61181 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3489 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#525 ◁ G | |
2032 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)(28,33)(29,40)(30,36)(31,44)(32,35)(34,41)(37,52)(38,48)(39,47)(42,51)(43,49)(45,50)(46,54)(53,56)(55,57);(18,20)(19,22)(21,25)(23,24)(26,28,32,39)(27,33,35,47)(29,37,42,55)(30,43,31,38)(34,46,50,56)(36,49,44,48)(40,52,51,57)(41,54,45,53);(26,29)(27,34)(28,37)(30,41)(31,45)(32,42)(33,46)(35,50)(36,51)(38,53)(39,55)(40,44)(43,54)(47,56)(48,52)(49,57);(20,25)(22,24)(27,35)(33,47)(34,50)(36,44)(40,51)(46,56)(48,49)(52,57);(26,30,32,31)(27,36,35,44)(28,38,39,43)(29,41,42,45)(33,48,47,49)(34,51,50,40)(37,53,55,54)(46,52,56,57)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54169);