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×#33863 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,23)(20,24,25,22)(26,27)(28,32)(29,33)(30,43)(31,36)(34,40)(35,41)(37,44)(38,53)(39,47)(42,49)(45,50)(46,51)(48,54)(52,56)(55,57);(18,20)(19,22)(21,25)(23,24)(26,28,31,39)(27,32,36,47)(29,37,42,52)(30,38,41,51)(33,44,49,56)(34,45,48,55)(35,46,43,53)(40,50,54,57);(27,33)(29,40)(30,41)(32,44)(34,35)(36,49)(37,50)(38,51)(42,54)(43,48)(45,46)(47,56)(52,57)(53,55);(20,25)(22,24)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26851);