Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#61110 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
2684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,27)(20,29,25,32)(21,31,22,26)(23,30,33,28);(18,20)(19,22)(21,27)(23,26)(24,25)(28,32)(29,30)(31,33);(18,21)(19,25)(20,27)(22,24)(23,32)(26,28)(29,33)(30,31);(18,22)(19,26)(20,30)(21,24)(23,32)(25,28)(27,31)(29,33);(19,27)(20,25)(26,31)(28,30)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54098);