Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60835 |
| 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 ◁ C4×#41×C17 ◁ G | |
2040 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)(26,27,30,35)(28,37,38,32)(29,41,42,34)(31,33,44,36)(39,46,51,50)(40,45,52,47)(43,49,54,48)(53,56,57,55);(18,20,21,25)(19,22,23,24)(26,28)(27,32)(29,39)(30,38)(31,40)(33,47)(34,46)(35,37)(36,45)(41,50)(42,51)(43,53)(44,52)(48,56)(49,55)(54,57);(20,25)(22,24)(27,33)(28,38)(31,44)(32,45)(34,48)(35,36)(37,47)(39,51)(41,49)(43,54)(46,55)(50,56);(19,23)(22,24)(26,29)(27,34)(28,39)(30,42)(31,43)(32,46)(33,48)(35,41)(36,49)(37,50)(38,51)(40,53)(44,54)(45,55)(47,56)(52,57);(28,38)(29,42)(32,37)(34,41)(40,52)(43,54)(45,47)(48,49)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53823);