Finite Group Databasebeta

← Prev (#88837) Next (#88839) →

Cayley diagram

C2×C3×C3⋊(C3⋊C8) #88838

order432
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C3⋊(C3⋊C8)
unambiguous semidirect product(C2×C3)⋊(C3×C3⋊C8)

Splittings

derivedC32 ⋊ C2×C3×C8
SylowC33 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4C3⋊D3
commutator, hypocenterC32C2×C3×C8
FrattiniC4C2×C3×C3⋊D3
FittingC2×C33×C4C2
socle, prime radicalC22×C33C4
cosocleC32×C4C22×C3
LCSG ▷ C32
UCSC1 ◁ C2×C3×C4

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2)(4,5)(7,8)(9,10,11)(12,13,14,16,15,17,18,19);(1,2)(3,4,5);(6,7,8)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic3×C3⋊C8, C3×#63554, C3×(C2×D3)⋊(C3⋊C8), …
maximal normal subgroup ofC3×Dic3×C3⋊C8, C3×#63554, C3×(C2×D3)⋊(C3⋊C8), …
maximal quotient ofC3×C4×C3⋊(C3⋊C8), C3×C4⋊(C3⋊(C3⋊C8)), C2×C3×C3⋊(C3⋊C16), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 485);