Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17968 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#3171 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#431 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(20,24)(21,23)(22,26)(25,29)(27,31)(28,30)(32,33)(34,35,38,42,39,36,43,41)(37,40,46,48,45,44,49,47);(19,23)(21,29)(24,30)(25,26)(28,33)(31,32)(34,36)(35,39)(37,44)(38,41)(40,45)(42,43)(46,47)(48,49);(18,20)(19,24)(21,28)(22,27)(23,30)(25,32)(26,31)(29,33)(34,37,38,46,39,45,43,49)(35,40,42,48,36,44,41,47);(20,27)(24,31)(28,33)(30,32)(35,36)(37,45)(41,42)(46,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10956);