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) = C2×C42 |
| direct product | C17×#7944 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
604 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)(20,27)(21,25)(22,31)(23,26)(24,28)(29,32)(30,33)(34,35)(36,42,44,39)(37,40)(38,41)(43,48,45,47)(46,49);(18,20)(19,24,26,33)(21,30)(22,28)(23,29)(25,27,31,32)(34,36)(35,39)(37,45)(38,44)(40,48)(41,42)(43,46)(47,49);(18,21,23,22)(19,25,26,31)(20,28,29,30)(24,32,33,27)(34,37,38,46)(35,40,41,49)(36,43,44,45)(39,47,42,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 932);