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) = C23×C4 |
| direct product | C17×#33908 |
| 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 | |
492 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)(26,27,32,36)(28,33,31,46)(29,39,41,55)(30,42,45,56)(34,49,51,40)(35,38,53,44)(37,54,47,52)(43,48,57,50);(18,20)(19,23)(21,24)(22,25)(26,28,32,31)(27,33,36,46)(29,37,41,47)(30,38,45,44)(34,48,51,50)(35,42,53,56)(39,54,55,52)(40,43,49,57);(18,21,22,19)(20,24,25,23)(26,29)(27,34)(28,37)(30,43)(31,47)(32,41)(33,48)(35,52)(36,51)(38,49)(39,42)(40,44)(45,57)(46,50)(53,54)(55,56);(20,25)(23,24)(26,28,32,31)(27,33,36,46)(29,37,41,47)(30,38,45,44)(34,48,51,50)(35,42,53,56)(39,54,55,52)(40,43,49,57)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26896);