Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1334 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)(18,19,25,28)(20,23,31,24)(21,32,36,29)(22,30,39,44)(26,34,41,35)(27,38,42,37)(33,40,48,49)(43,46,45,47);(18,20,23,28,25,31,24,19)(21,26,34,29,36,41,35,32)(22,30,37,42,39,44,38,27)(33,40,46,43,48,49,47,45);(18,21)(19,26)(20,29)(22,33)(23,34)(24,35)(25,36)(27,40)(28,41)(30,43)(31,32)(37,46)(38,47)(39,48)(42,49)(44,45);(18,22,24,38,25,39,23,37)(19,27,31,44,28,42,20,30)(21,33,35,47,36,48,34,46)(26,40,32,45,41,49,29,43)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17285);