Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#21776 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2308 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C17×#3484 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C24×C17 ◁ G | |
1520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,23)(21,29,30,24)(22,25)(27,31)(32,33);(18,20)(19,23)(21,27)(22,28)(24,31)(25,26)(29,32)(30,33);(23,26)(31,32);(18,21)(19,24)(20,27)(22,30)(23,31)(25,29)(26,32)(28,33)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14764);