Finite Group Databasebeta

← Prev (#88919) Next (#88921) →

Cayley diagram

Dic3×#157 #88920

order432
isoclinismisoclinic class of D3×#157
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C3×C4

Aliases

direct productDic3×#157

Splittings

derived, SylowC33 ⋊ C42

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D3×#157
commutator, hypocenterC33C42
Fitting, socleC2×C33C2×C4
prime radical, cosocleC2×C3×C3⋊D3C22
LCSG ▷ C33
UCSC1 ◁ C2

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 2 generators on 13 points:

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

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×AGL(1,𝔽9), Dic3⋊AGL(1,𝔽9), Dic3×GO+(4,𝔽2), …
maximal normal subgroup ofDic3×AGL(1,𝔽9), Dic3⋊AGL(1,𝔽9), Dic3×GO+(4,𝔽2), …
maximal quotient ofC3⋊C8×#157, #11722703, #11722704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 567);