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×#17629 |
| 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×#3506 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1010 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)(19,25,27,40)(20,30)(22,36)(26,39,43,42)(28,41,29,37)(31,46)(32,33)(44,49,45,48);(18,19)(20,25)(21,26)(22,37)(23,28)(24,29)(27,38)(30,41)(31,39)(32,42)(33,48)(34,44)(35,45)(36,40)(43,47)(46,49);(18,20,24,22)(19,25,29,37)(21,32,35,46)(23,30,38,36)(26,42,45,49)(27,40,28,41)(31,34,33,47)(39,44,48,43);(18,21,24,35)(19,26,29,45)(20,31,22,33)(23,34,38,47)(25,39,37,48)(27,43,28,44)(30,46,36,32)(40,42,41,49)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10617);