Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33638 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C2×#476 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
514 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)(19,25)(20,30,32,48)(21,23)(22,34)(26,40,41,44)(27,29)(31,35,37,47)(33,36)(38,42,46,49)(39,45);(18,19,21,25,24,27,23,29)(20,26,31,38,32,41,37,46)(22,28,33,39,36,43,34,45)(30,42,47,40,48,49,35,44);(18,20)(19,26)(21,31)(22,35)(23,37)(24,32)(25,38)(27,41)(28,44)(29,46)(30,33)(34,48)(36,47)(39,42)(40,43)(45,49);(19,27)(25,29)(26,41)(28,43)(38,46)(39,45)(40,44)(42,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26626);