Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12940 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
424 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)(18,19,21,20)(22,23)(24,35)(25,40)(26,30)(27,45)(28,34)(29,36)(31,41)(32,43)(33,42)(37,52)(38,47)(39,51)(44,50)(46,48)(49,53);(18,20,21,19)(22,24)(23,29)(25,37)(26,44)(27,46)(28,39)(30,47)(31,48)(32,51)(33,52)(34,50)(35,40)(36,41)(38,42)(43,53)(45,49);(23,30)(25,41)(26,43)(27,42)(29,47)(31,34)(32,45)(33,40)(35,52)(36,37)(38,46)(44,53)(48,50)(49,51)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5928);