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Cayley diagram

C2×A4×D7 #66748

order336
isoclinismisoclinic class of A4×D7
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×A4×D7

Splittings

Fitting, socleC23×C7 ⋊ C2×C3
derivedC22×C7 ⋊ C22×C3
HallC23×D7 ⋊ C3
SylowC7 ⋊ C22×A4

Subgroups

subgroupG/H
center, hypercenterC2A4×D7
commutator, cosocle, hypocenterC22×C7C22×C3
FrattiniC1G
Fitting, socleC23×C7C2×C3
LCSG ▷ C22×C7
UCSC1 ◁ C2

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 42

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

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×SL(2,ℤ/4), #10621482, #10621483, …
maximal normal subgroup ofD7×SL(2,ℤ/4), #10621482, #10621483, …
maximal quotient ofA4×Dic14, C4×A4×D7, A4×D28, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 217);