Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61178 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#525 ◁ G | |
2090 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(28,36)(29,30)(32,39)(33,35)(37,38)(40,41);(18,20)(19,22)(21,25)(23,24)(26,27)(28,32)(29,33)(30,35)(31,34)(36,39)(37,40)(38,41);(26,28,31,37)(27,32,34,40)(29,36,30,38)(33,39,35,41);(20,25)(22,24)(26,29,31,30)(27,33,34,35)(28,36,37,38)(32,39,40,41);(27,34)(32,40)(33,35)(39,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54166);