Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C2×D8×C17 | C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
458 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,21)(20,24,25,23)(26,27,29,34)(28,37,38,32)(30,33,41,49)(31,44,42,36)(35,51,50,43)(39,45,54,48)(40,47,55,53)(46,57,52,56);(18,20,22,25)(19,23,21,24)(26,28,29,38)(27,32,34,37)(30,39,41,54)(31,40,42,55)(33,48,49,45)(35,46,50,52)(36,47,44,53)(43,57,51,56);(27,33)(28,38)(30,43)(31,42)(32,45)(34,49)(35,36)(37,48)(39,56)(41,51)(44,50)(46,53)(47,52)(54,57);(18,21,22,19)(20,23,25,24)(28,38)(32,37)(39,54)(40,55)(45,48)(46,52)(47,53)(56,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26943);