Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9092 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(18,19,22,24,21,20,23,25)(26,27)(28,37)(29,41,44,51)(30,45)(31,35)(32,36)(33,39)(34,43,50,42)(38,53,55,47)(40,48)(46,49)(52,54,57,56);(18,20,22,25,21,19,23,24)(26,28,30,39,32,40,31,46)(27,33,35,37,36,49,45,48)(29,38,43,56,44,55,42,54)(34,47,51,52,50,53,41,57);(19,20)(24,25)(26,29,32,44)(27,34,36,50)(28,38,40,55)(30,43,31,42)(33,47,49,53)(35,51,45,41)(37,52,48,57)(39,56,46,54)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2080);