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×#17623 |
| 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×#3505 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1014 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)(19,25,28,42)(20,31)(22,35)(26,44,45,47)(27,41,40,46)(29,43,30,38)(32,48)(34,36);(18,19)(20,26)(21,27)(22,38)(23,29)(24,30)(25,32)(28,39)(31,41)(33,47)(34,46)(35,42)(36,45)(37,44)(40,49)(43,48);(18,20)(19,26)(21,35)(22,33)(23,31)(24,34)(25,40)(27,42)(28,45)(29,41)(30,46)(32,49)(36,39)(37,48)(38,47)(43,44);(18,21,23,33)(19,27,29,47)(20,32,31,48)(22,36,35,34)(24,37,39,49)(25,41,43,26)(28,40,30,44)(38,45,42,46)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10611);