Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7943 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#7954 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C24×C17 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,27,21,25)(20,28,29,32,31,33,30,24)(34,35)(36,44,47,48)(37,41)(38,42)(39,43)(40,46,49,45);(18,20)(19,24,27,32)(21,30)(22,29)(23,31)(25,33,26,28)(34,36)(35,40,43,49)(37,45)(38,46)(39,47)(41,48,42,44);(18,21,23,22)(19,25,27,26)(20,29,31,30)(24,28,32,33)(34,37,39,38)(35,41,43,42)(36,45,47,46)(40,48,49,44)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 942);