Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12941 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
388 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,29)(24,34)(25,26)(27,39)(30,46)(31,32)(33,45)(35,36)(37,53)(38,42)(40,41)(43,52)(44,48)(49,50);(18,20,21,19)(22,23)(24,30)(25,38)(26,29)(27,42)(28,33)(31,40)(32,39)(34,47)(35,44)(36,46)(37,50)(41,45)(43,49)(48,52)(51,53);(22,24,28,37)(23,30,33,50)(25,34,40,53)(26,35,41,52)(27,43,39,36)(29,44,45,48)(31,51,38,47)(32,46,42,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5929);