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ΓL(1,𝔽8)×D265 #26013288

order11130
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D265
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D53)
unambiguous semidirect productC53⋊(D5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D265)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C53 ⋊ C2×C3
HallC5×ΓL(1,𝔽8)×C53 ⋊ C2
HallC7×D265 ⋊ C3
HallΓL(1,𝔽8)×C53 ⋊ D5
HallC7×C53 ⋊ C3×D5
HallC5×C53 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ D53
SylowC53 ⋊ D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D53
SylowC7 ⋊ C3×D265
SylowC5 ⋊ ΓL(1,𝔽8)×D53

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C53C2×C3
LCSG ▷ C5×C7×C53
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

670 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊#11761505, ΓL(1,𝔽8)⋊#11761506, ΓL(1,𝔽8)×#11761505, …
maximal normal subgroup ofΓL(1,𝔽8)⋊#11761505, ΓL(1,𝔽8)⋊#11761506, ΓL(1,𝔽8)×#11761505, …
maximal quotient ofΓL(1,𝔽8)×Dic265, C2×ΓL(1,𝔽8)×D265, C7⋊C9×D265, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 22);