Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8412 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#8415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3515 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23,24,25)(26,27)(28,36,39,32)(29,40,42,49)(30,35)(31,34)(33,41,47,43)(37,52)(38,51,56,46)(44,48)(45,53)(50,55)(54,57);(18,19)(20,23)(21,25)(22,24)(26,28)(27,32)(29,37)(30,38)(31,39)(33,45)(34,36)(35,46)(40,57)(41,53)(42,54)(43,55)(44,56)(47,50)(48,51)(49,52);(18,20,22,21)(19,23,24,25)(26,29,31,42)(27,33,34,47)(28,37,39,54)(30,43,44,41)(32,45,36,50)(35,49,48,40)(38,55,56,53)(46,52,51,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1403);