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ΓL(1,𝔽8)×D221 #22604654

order9282
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D221
unambiguous semidirect productC17⋊(ΓL(1,𝔽8)×D13)

Splittings

Fitting, socle, derived, HallC7×C13×C17 ⋊ C2×C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C2
HallC7×D221 ⋊ C3
HallC17×ΓL(1,𝔽8) ⋊ D13
HallC13×ΓL(1,𝔽8) ⋊ D17
HallC13×C17 ⋊ C2×ΓL(1,𝔽8)
HallC7×C17 ⋊ C3×D13
HallC7×C13 ⋊ C3×D17
SylowC17 ⋊ ΓL(1,𝔽8)×D13
SylowC13 ⋊ ΓL(1,𝔽8)×D17
SylowC7 ⋊ C3×D221

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C13×C17C2×C3
LCSG ▷ C7×C13×C17
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊#11725130, ΓL(1,𝔽8)⋊#11725131, AGL(1,𝔽7)×D221, …
maximal normal subgroup ofΓL(1,𝔽8)⋊#11725130, ΓL(1,𝔽8)⋊#11725131, AGL(1,𝔽7)×D221, …
maximal quotient ofΓL(1,𝔽8)×Dic221, C2×ΓL(1,𝔽8)×D221, C7⋊C9×D221, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 30);