Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17967 |
| 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×#121 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
594 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)(20,26)(21,29)(22,24)(23,27)(25,31)(28,33)(30,32)(34,35,39,42,38,41,47,49)(36,43,45,46,44,40,48,37);(18,20,22,28)(19,23,24,32)(21,30,31,27)(25,33,29,26)(34,36)(35,40)(37,42)(38,44)(39,45)(41,43)(46,49)(47,48);(19,24)(23,32)(25,29)(26,33)(34,37,39,43,38,46,47,40)(35,36,42,45,41,44,49,48);(19,24)(23,32)(25,29)(26,33)(35,41)(36,44)(42,49)(45,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10955);