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×#33968 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#2250 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
516 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)(19,23)(24,25)(26,27)(28,37)(29,34)(30,42)(31,46)(32,36)(33,40)(35,44)(38,53)(39,54)(41,52)(43,49)(45,56)(47,51)(48,55)(50,57);(18,19,22,23)(20,24,21,25)(28,38)(33,48)(37,53)(39,47)(40,55)(43,57)(49,50)(51,54);(18,20,22,21)(19,24,23,25)(26,28)(27,33)(29,39)(30,43)(31,47)(32,38)(34,49)(35,51)(36,48)(37,42)(40,44)(41,55)(45,57)(46,50)(52,54)(53,56);(18,21,22,20)(19,24,23,25)(26,29,32,31)(27,34,36,46)(28,39,38,47)(30,41,45,44)(33,49,48,50)(35,42,52,56)(37,54,53,51)(40,43,55,57)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26956);