Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C23×C42 |
| direct product | C17×#21826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
1050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35)(36,42,44,39)(37,40)(38,41)(43,48,49,46)(45,47);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,36)(35,39)(37,43)(38,44)(40,46)(41,42)(45,49)(47,48);(19,25)(23,26)(24,33)(31,32)(34,37,38,45)(35,40,41,47)(36,43,44,49)(39,46,42,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14814);