Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11178 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #388 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1440 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,30)(21,35,39,43)(22,28)(23,27)(24,29)(25,32)(26,37,44,38)(31,46,48,40)(33,41)(34,45)(36,49,47,42);(18,20)(19,25)(21,36)(22,33)(23,32)(24,34)(26,42)(27,45)(28,30)(29,41)(31,38)(35,46)(37,48)(39,47)(40,43)(44,49);(18,21,22,37,24,39,23,38)(19,26,27,43,29,44,28,35)(20,31,32,47,34,48,33,36)(25,40,30,42,41,46,45,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4166);