Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60175 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×C17×#578 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
2650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(24,32)(25,30)(26,38)(27,29)(28,34)(31,40)(33,46)(35,45)(36,43)(37,50)(39,41)(42,48)(44,49)(47,53)(51,52);(22,24,27,35)(23,28,29,41)(25,33,36,47)(26,39,40,34)(30,42,43,52)(31,45,38,32)(37,51,49,48)(44,53,50,46);(18,20,21,19)(23,29)(28,41)(30,43)(31,38)(32,45)(42,52)(44,50)(46,53);(22,25)(23,30)(24,33)(26,37)(27,36)(28,42)(29,43)(31,44)(32,46)(34,48)(35,47)(38,50)(39,51)(40,49)(41,52)(45,53);(25,36)(30,43)(33,47)(37,49)(42,52)(44,50)(46,53)(48,51)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53163);