Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10224 |
| 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 | |
462 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)(18,19,24,28)(20,29,21,32)(22,27,23,26)(25,31,33,30)(36,43)(37,38)(40,44)(41,47)(45,46)(48,49);(18,20,24,21)(19,25,28,33)(22,31,23,30)(26,32,27,29)(34,35)(36,44)(37,41)(38,47)(39,42)(40,46)(43,48)(45,49);(18,21,24,20)(19,25,28,33)(22,30,23,31)(26,32,27,29)(34,36)(35,40)(37,46)(38,43)(39,45)(41,49)(42,48)(44,47)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3212);