Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#8488 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C17×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
768 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)(20,21,25,23)(22,24)(26,27,31,36,32,37,30,35)(28,38,42,33,41,48,40,47)(29,34,43,49,44,50,45,51)(39,53,54,57,55,52,56,46);(18,20)(19,23)(21,24)(22,25)(26,28)(27,33)(29,39)(30,42)(31,40)(32,41)(34,46)(35,48)(36,38)(37,47)(43,56)(44,55)(45,54)(49,52)(50,57)(51,53);(18,21,22,23)(19,20,24,25)(26,29)(27,34)(28,39)(30,45)(31,43)(32,44)(33,46)(35,51)(36,49)(37,50)(38,52)(40,56)(41,55)(42,54)(47,57)(48,53)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1476);