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C3×C4×ΓL(1,𝔽8)×C73 #32913805

order18396
automorphism?
homologyAbelianization (H1) = C32×C4×C73 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×ΓL(1,𝔽8)×C73
unambiguous semidirect product(C4×C7)⋊(C32×C73)
unambiguous semidirect product(C3×C4×C7)⋊(C3×C73)

Splittings

FittingC3×C4×C7×C73 ⋊ C3
derived, SylowC7 ⋊ C32×C4×C73
HallC4×C7×C73 ⋊ C32
HallC7×C73 ⋊ C32×C4
HallC4×C7 ⋊ C32×C73

Subgroups

subgroupG/H
center, hypercenterC3×C4×C73ΓL(1,𝔽8)
commutator, hypocenterC7C32×C4×C73
FrattiniC2C2×C3×ΓL(1,𝔽8)×C73
FittingC3×C4×C7×C73C3
socleC2×C3×C7×C73C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C73C2
cosocleC2×C7C2×C32×C73
LCSG ▷ C7
UCSC1 ◁ C3×C4×C73

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6132

Conjugacy classes & character table

4380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18396, 123);