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C3×C29×ΓL(1,𝔽8)⋊C4 #20300585

order7308
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C32×C4×C29 · Schur multiplier (H2) = C3

Aliases

direct productC3×C29×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C29)
unambiguous semidirect productDic7⋊(C32×C29)
unambiguous semidirect product(C3×Dic7)⋊(C3×C29)
unambiguous semidirect product(Dic7×C29)⋊C32
unambiguous semidirect product(C3×Dic7×C29)⋊C3

Splittings

derived, SylowC7 ⋊ C32×C4×C29
HallC3×ΓL(1,𝔽8)×C29 ⋊ C4
HallDic7×C29 ⋊ C32
HallC7×C29 ⋊ C32×C4
HallC3×ΓL(1,𝔽8) ⋊ C4×C29
HallDic7 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29AGL(1,𝔽7)
commutator, hypocenterC7C32×C4×C29
FrattiniC2C3×C29×AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C29C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C3×C29

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 60);