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C3×C4×ΓL(1,𝔽8)×C29 #20300592

order7308
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C32×C4×C29 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×ΓL(1,𝔽8)×C29
unambiguous semidirect product(C4×C7)⋊(C32×C29)
unambiguous semidirect product(C3×C4×C7)⋊(C3×C29)
unambiguous semidirect product(C4×C7×C29)⋊C32
unambiguous semidirect product(C3×C4×C7×C29)⋊C3

Splittings

FittingC3×C4×C7×C29 ⋊ C3
derived, SylowC7 ⋊ C32×C4×C29
HallC4×C7×C29 ⋊ C32
HallC7×C29 ⋊ C32×C4
HallC4×C7 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC3×C4×C29ΓL(1,𝔽8)
commutator, hypocenterC7C32×C4×C29
FrattiniC2C2×C3×ΓL(1,𝔽8)×C29
FittingC3×C4×C7×C29C3
socleC2×C3×C7×C29C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C4×C29

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×Dic5×ΓL(1,𝔽8)×C29, C3×C4×C5×ΓL(1,𝔽8)×C29, C3×AGL(1,𝔽5)×ΓL(1,𝔽8)×C29
maximal normal subgroup ofC3×C4×C5×ΓL(1,𝔽8)×C29
maximal quotient ofC3×Dic5×ΓL(1,𝔽8)×C29, C3×C4×C5×ΓL(1,𝔽8)×C29, C3×AGL(1,𝔽5)×ΓL(1,𝔽8)×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 67);