Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10207 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #127 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
474 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,24,29)(20,30,21,32)(22,28,23,27)(25,33,26,31)(35,40)(37,38)(41,44)(42,43)(45,46)(48,49);(18,20,24,21)(19,25,29,26)(22,33,23,31)(27,32,28,30)(34,35,39,43)(36,44,47,48)(37,42,38,40)(41,45,49,46);(18,21,24,20)(19,26,29,25)(22,33,23,31)(27,32,28,30)(34,36,39,47)(35,41,43,49)(37,46,38,45)(40,44,42,48)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3195);