Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17841 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C22×C4⋊C4 |
| prime radical | C2×#41×C17 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G | |
592 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)(21,25)(22,32)(23,26)(24,30)(28,29)(31,33)(34,35,38,42,39,43,37,41)(36,44,47,48,45,49,46,40);(18,20,21,29,23,31,22,30)(19,24,32,33,26,28,25,27)(34,36,38,47,39,45,37,46)(35,40,41,49,43,48,42,44);(18,19)(20,28)(21,32)(22,25)(23,26)(24,31)(27,29)(30,33)(36,45)(40,48)(44,49)(46,47);(18,21,23,22)(19,25,26,32)(20,29,31,30)(24,27,28,33)(34,37,39,38)(35,41,43,42)(36,46,45,47)(40,49,48,44)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10829);