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Cayley diagram

C3×A4×D7 #92755

order504
isoclinismisoclinic class of A4×D7
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×D7

Splittings

Fitting, socleC22×C3×C7 ⋊ C2×C3
derivedC22×C7 ⋊ C2×C32
HallC22×D7 ⋊ C32
SylowC7 ⋊ C2×C3×A4

Subgroups

subgroupG/H
center, hypercenterC3A4×D7
commutator, cosocle, hypocenterC22×C7C2×C32
FrattiniC1G
Fitting, socleC22×C3×C7C2×C3
LCSG ▷ C22×C7
UCSC1 ◁ C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 84

A minimal faithful permutation representation — 2 generators on 14 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D7×S4, D7×C3⋊S4, D3×A4×D7, …
maximal normal subgroup ofC3×D7×S4, D7×C3⋊S4, D3×A4×D7, …
maximal quotient ofC3×#66662, C3×D7×SL(2,𝔽3), C3×A4×Dic7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 181);