Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17597 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3519 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,24,26,37)(20,29)(21,32)(25,39,41,48)(27,38,28,33)(30,43)(31,46)(34,47)(36,40,49,42)(44,45);(18,19)(20,25)(21,33)(22,27)(23,28)(24,34)(26,35)(29,42)(30,40)(31,39)(32,37)(36,44)(38,47)(41,43)(45,49)(46,48);(18,20)(19,25)(21,31)(22,30)(23,29)(24,36)(26,41)(27,40)(28,42)(32,45)(33,39)(34,44)(35,43)(37,49)(38,48)(46,47);(20,30)(25,40)(29,43)(31,45)(36,48)(39,49)(41,42)(44,46)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10585);