Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#24420 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1326 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)(18,19,22,28,24,25,23,29)(20,30,34,39,33,41,31,26)(21,35,36,43,37,27,38,42)(32,44,45,40,46,49,47,48);(19,25)(20,31)(22,23)(26,30)(27,35)(32,45)(33,34)(36,38)(39,41)(40,44)(46,47)(48,49);(18,20)(19,26)(21,32)(22,31)(23,34)(24,33)(25,39)(27,40)(28,41)(29,30)(35,48)(36,47)(37,46)(38,45)(42,44)(43,49);(18,21)(19,27)(20,32)(22,38)(23,36)(24,37)(25,35)(26,40)(28,43)(29,42)(30,44)(31,45)(33,46)(34,47)(39,48)(41,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17408);