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C5×ΓL(1,𝔽8)×C97 #23779161

order10185
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C3×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×C97
unambiguous semidirect productC7⋊(C3×C5×C97)
unambiguous semidirect product(C5×C7)⋊(C3×C97)

Splittings

Fitting, socle, HallC5×C7×C97 ⋊ C3
derived, SylowC7 ⋊ C3×C5×C97
HallC7×C97 ⋊ C3×C5
HallC5×C7 ⋊ C3×C97

Subgroups

subgroupG/H
center, hypercenterC5×C97ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C5×C97
FrattiniC1G
Fitting, socleC5×C7×C97C3
LCSG ▷ C7
UCSC1 ◁ C5×C97

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2425 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)×C97, C5×ΓL(1,𝔽8)×D97, C5×AGL(1,𝔽7)×C97, …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)×C97, C5×ΓL(1,𝔽8)×D97, C5×AGL(1,𝔽7)×C97, …
maximal quotient ofC2×C5×ΓL(1,𝔽8)×C97, C5×C7⋊C9×C97, C3×C5×ΓL(1,𝔽8)×C97

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10185, 3);