Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60167 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C23×D4 |
| prime radical | C22×C17×#135 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#117 ◁ G | |
2706 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(24,33)(25,30)(26,32)(27,40)(28,31)(29,35)(34,47)(36,44)(37,46)(38,45)(39,50)(41,43)(42,49)(48,52)(51,53);(22,24)(23,29)(25,34)(26,35)(27,41)(28,36)(30,42)(31,43)(32,44)(33,40)(37,48)(38,49)(39,51)(45,52)(46,53)(47,50);(18,20,21,19)(22,25)(23,30)(24,34)(26,38)(27,39)(28,37)(29,42)(31,46)(32,45)(33,47)(35,49)(36,48)(40,50)(41,51)(43,53)(44,52);(23,31)(25,37)(29,43)(32,40)(33,44)(34,48)(38,39)(49,51);(22,26,28,27)(23,32,31,40)(24,35,36,41)(25,38,37,39)(29,44,43,33)(30,45,46,50)(34,49,48,51)(42,52,53,47)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53155);