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×#17598 |
| 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×#3520 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
996 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)(19,24,26,38)(20,29)(21,32)(25,40,42,48)(27,39,28,33)(30,44)(31,47)(34,36)(37,41,49,43)(45,46);(18,19,22,27)(20,25,30,41)(21,33,32,38)(23,28,35,26)(24,36,39,34)(29,43,44,42)(31,40,46,49)(37,47,48,45);(18,20)(19,25)(21,31)(22,30)(23,29)(24,37)(26,42)(27,41)(28,43)(32,46)(33,40)(34,45)(35,44)(36,47)(38,49)(39,48);(20,30)(25,41)(29,44)(31,46)(37,48)(40,49)(42,43)(45,47)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10586);