Finite Group DatabasebetaFinite Group Databasebeta| order | 456 |
| isoclinism | isoclinic class of #90695 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C19 ⋊ Q8 |
| Sylow | C19 ⋊ Dic6 |
| Sylow | C3 ⋊ Dic38 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D19 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C19 | C22 |
| hypocenter | C3×C19 | Q8 |
| LCS | G ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 456 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(21,22)(23,25,26,30)(24,27,28,29);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,22)(23,24,26,28)(25,29,30,27)Polycyclic presentation:
2^3,3,19|a^2=c,b^2=c,b^a=bc,e^a=e^18,d^b=d^263 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×D19, D3×Dic38, D57⋊Q8, … |
| maximal normal subgroup of | Dic6×D19, D3×Dic38, D57⋊Q8, … |
| maximal quotient of | Dic19⋊Dic3, #11744835, Dic3⋊Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(456, 18);