Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#8500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #379 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#3546 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
736 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)(20,27,29,23)(21,26)(22,25)(24,28,32,30)(31,33)(34,35,38,41,39,43,37,42)(36,44,45,40,46,48,47,49);(18,20)(19,23)(21,28)(22,29)(24,26)(25,27)(30,31)(32,33)(34,36)(35,40)(37,47)(38,45)(39,46)(41,48)(42,44)(43,49);(18,20)(19,24)(21,30)(22,29)(23,26)(25,32)(27,33)(28,31)(35,41)(37,38)(40,48)(42,43)(44,49)(45,47)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1488);