Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11281 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #397 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(22,23)(24,33)(25,37)(26,42)(27,31)(28,32)(29,35)(30,40)(34,47)(36,45)(38,52)(39,48)(41,51)(43,46)(44,53)(49,50);(22,24)(23,29)(25,38,40,53)(26,43)(27,35)(28,36)(30,47,37,49)(31,45)(32,46)(33,42)(34,41,50,39)(44,48,52,51);(22,25,26,39,28,40,27,41)(23,30,31,48,32,37,42,51)(24,34,35,38,36,50,43,53)(29,44,33,49,46,52,45,47)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4269);