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×#8431 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
696 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)(18,19,22,24,23,20,21,25)(26,27,31,37,32,35,30,36)(28,38,40,51,41,33,46,48)(29,42,44,34,45,50,43,49)(39,53,54,47,55,57,56,52);(18,20)(19,23)(21,25)(22,24)(26,28)(27,33)(29,39)(30,40)(31,46)(32,41)(34,47)(35,38)(36,48)(37,51)(42,57)(43,54)(44,56)(45,55)(49,52)(50,53);(18,21,23,22)(19,24,20,25)(26,29,32,45)(27,34,35,49)(28,39,41,55)(30,44,31,43)(33,47,38,52)(36,50,37,42)(40,56,46,54)(48,53,51,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1419);