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Cayley diagram

C2×C3⋊SL(2,ℤ/4) #64268

order288
isoclinismisoclinic class of C3⋊S4
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC2×C3⋊SL(2,ℤ/4)
unambiguous semidirect product(C2×C3)⋊SL(2,ℤ/4)
unambiguous semidirect product(C2×A4)⋊Dic3

Splittings

derivedC3×A4 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22C3⋊S4
commutator, hypocenterC3×A4C2×C4
FrattiniC2C2×C3⋊S4
Fitting, socleC24×C3D3
prime radicalC22×C3×A4C2
cosocleC2×C3×A4C22
LCSG ▷ C3×A4
UCSC1 ◁ C22

158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 72

A minimal faithful permutation representation — 3 generators on 13 points:

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

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×SL(2,ℤ/4), #10593238, SL(2,ℤ/4)⋊Dic3, …
maximal normal subgroup ofDic3×SL(2,ℤ/4), #10593238, SL(2,ℤ/4)⋊Dic3, …
maximal quotient ofC2×C3⋊(A4⋊C8), #10593643, C4×C3⋊SL(2,ℤ/4), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 916);