Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#2206 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×Q8×C17 ◁ C8×Q8×C17 ◁ G | |
520 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)(26,27,31,36)(28,32,39,47)(29,33,42,49)(30,43,41,35)(34,50,48,40)(37,44,53,56)(38,54,52,46)(45,57,55,51);(18,19,22,23)(20,24,21,25)(26,28,31,39)(27,32,36,47)(29,37,42,53)(30,38,41,52)(33,44,49,56)(34,45,48,55)(35,46,43,54)(40,51,50,57);(18,20,22,21)(19,24,23,25)(27,33)(29,40)(30,41)(32,44)(34,35)(36,49)(37,51)(38,52)(42,50)(43,48)(45,46)(47,56)(53,57)(54,55);(18,21,22,20)(19,24,23,25)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26949);