Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11018 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #386 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
1270 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)(22,23,27,31,28,33,26,32)(24,34,36,29,37,44,42,45)(25,30,40,47,41,48,39,49)(35,46,50,43,51,53,38,52);(22,24)(23,29)(25,38)(26,42)(27,36)(28,37)(30,46)(31,44)(32,34)(33,45)(35,40)(39,51)(41,50)(43,47)(48,53)(49,52);(19,21)(22,25)(23,30)(24,35)(26,39)(27,40)(28,41)(29,43)(31,47)(32,49)(33,48)(34,46)(36,50)(37,51)(38,42)(44,53)(45,52)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4006);