Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61628 |
| 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 | |
2114 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)(20,24)(21,23)(22,25)(26,27)(28,38)(29,33)(30,35)(31,37)(32,36)(34,40)(39,41);(18,20)(19,22)(21,25)(23,24)(26,28,31,29)(27,33,37,38)(30,40,32,39)(34,35,41,36);(26,29,31,28)(27,34,37,41)(30,40,32,39)(33,35,38,36);(20,25)(22,24)(26,30,31,32)(27,35,37,36)(28,39,29,40)(33,34,38,41);(19,23)(22,24)(26,30,31,32)(27,36,37,35)(28,39,29,40)(33,41,38,34)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54616);