Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#21477 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #120 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C4×#120 |
| prime radical | C17×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
1290 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)(18,19,25,28,24,29,23,39)(20,30,33,26,34,43,40,44)(21,35,36,38,37,27,41,22)(31,45,47,42,48,32,46,49);(18,20)(19,26)(21,31)(22,32)(23,40)(24,34)(25,33)(27,42)(28,43)(29,44)(30,39)(35,49)(36,47)(37,48)(38,45)(41,46);(18,21)(19,27)(20,31)(22,28)(23,41)(24,37)(25,36)(26,42)(29,35)(30,45)(32,43)(33,47)(34,48)(38,39)(40,46)(44,49);(18,22,25,35,24,38,23,27)(19,21,28,36,29,37,39,41)(20,32,33,49,34,45,40,42)(26,31,43,47,44,48,30,46)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14465);