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×#21780 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2308 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3486 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,22,27,23,26,37,41)(20,28,31,42,30,24,35,39)(21,32,33,43,34,25,36,40)(29,38,46,48,45,44,47,49);(18,20)(19,24)(21,29)(22,35)(23,30)(25,38)(26,28)(27,42)(31,37)(32,44)(33,47)(34,45)(36,46)(39,41)(40,49)(43,48);(24,28)(38,44)(39,42)(48,49);(18,21,23,34)(19,25,26,32)(20,29,30,45)(22,36,37,33)(24,38,28,44)(27,43,41,40)(31,47,35,46)(39,49,42,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14768);