Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#17385 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C42×C17 ◁ G | |
988 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(20,28,31,24)(21,25)(22,26)(23,27)(29,33,30,32)(34,35,38,42,39,43,37,41)(36,40,46,49,44,47,45,48);(18,20,23,31)(19,24,27,28)(21,29,22,30)(25,32,26,33)(34,36)(35,40)(37,45)(38,46)(39,44)(41,48)(42,49)(43,47);(18,21,23,22)(19,25,27,26)(20,29,31,30)(24,32,28,33)(36,44)(40,47)(45,46)(48,49);(18,22,23,21)(19,26,27,25)(20,30,31,29)(24,33,28,32)(34,37,39,38)(35,41,43,42)(36,45,44,46)(40,48,47,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10373);