Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33841 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,27,32)(24,33,34,45)(25,38,41,47)(26,29,40,31)(28,43,44,36)(30,48,50,39)(35,51,52,46)(37,53,42,49);(22,24,27,34)(23,28,32,44)(25,35,41,52)(26,42,40,37)(29,46,31,51)(30,49,50,53)(33,47,45,38)(36,48,43,39);(19,21)(24,34)(28,44)(33,45)(35,52)(36,43)(37,42)(46,51)(49,53);(23,29)(24,35)(25,39)(26,40)(28,45)(31,32)(33,44)(34,52)(36,37)(38,47)(41,48)(42,43)(46,49)(51,53)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26829);