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C5×C19×ΓL(1,𝔽8)⋊C4 #22547601

order7980
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C19×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C5×C19)
unambiguous semidirect productDic7⋊(C3×C5×C19)
unambiguous semidirect product(C5×Dic7)⋊(C3×C19)

Splittings

derived, SylowC7 ⋊ C3×C4×C5×C19
HallC5×C19×Dic7 ⋊ C3
HallC5×C19×ΓL(1,𝔽8) ⋊ C4
HallC5×C7×C19 ⋊ C3×C4
HallC19×Dic7 ⋊ C3×C5
HallC19×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×Dic7 ⋊ C3×C19
HallC7×C19 ⋊ C3×C4×C5
HallC5×ΓL(1,𝔽8) ⋊ C4×C19
HallC5×C7 ⋊ C3×C4×C19
HallDic7 ⋊ C3×C5×C19
HallΓL(1,𝔽8) ⋊ C4×C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C5×C19
FrattiniC2C5×C19×AGL(1,𝔽7)
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C19⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×C19×ΓL(1,𝔽8)⋊C4, C5×C19×C3⋊(ΓL(1,𝔽8)⋊C4)
maximal normal subgroup ofC5×C19⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×C19×ΓL(1,𝔽8)⋊C4
maximal quotient ofC5×C19×Dic7⋊C9, C3×C5×C19×ΓL(1,𝔽8)⋊C4, C5×C19×C3⋊(ΓL(1,𝔽8)⋊C4)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 26);