Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17963 |
| 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×#466 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
614 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)(20,27)(21,26)(22,30)(23,25)(24,28)(29,33)(31,32)(34,35,39,42,40,36,38,43)(37,44,46,49,47,41,45,48);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,36)(35,40)(37,44)(38,42)(39,43)(41,47)(45,48)(46,49);(19,25)(24,32)(26,30)(27,33)(34,37,39,46,40,47,38,45)(35,41,42,48,36,44,43,49);(18,21,23,22)(19,26,25,30)(20,28,29,31)(24,33,32,27)(34,38,40,39)(35,42,36,43)(37,45,47,46)(41,48,44,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10951);