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D3×#13047 #72248504

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD3×#13047

Splittings

FittingC3×#13047 ⋊ C2
SylowC3 ⋊ C2×#13047

Subgroups

subgroupG/H
centerC22D3×B(4,𝔽2)
commutatorC2×C3×D4C23×C4
FrattiniC22×D4C23×D3
FittingC3×#13047C2
socleC22×C3C2×B(4,𝔽2)
prime radicalC2×D3×#453C2
cosocleC22×C3×D4C24
hypercenter#13047D3
hypocenterC3C2×#13047
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #13047

5476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 4 generators on 15 points:

(14,15);(1,3,4,2)(7,11)(13,14,15);(1,2,4,3)(5,6)(7,9,11,12)(8,10);(6,9,10,12)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#494600
maximal normal subgroup ofD3×#494600
maximal quotient ofD3×#139706

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((14,15), (1,3,4,2)(7,11)(13,14,15), (1,2,4,3)(5,6)(7,9,11,12)(8,10), (6,9,10,12));