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ΓL(1,𝔽8)×D455 #34062171

order19110
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D455
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D91)

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C2×C3
HallC5×C7×C13×ΓL(1,𝔽8) ⋊ C2
HallC7×D455 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ D5
HallC5×C7×ΓL(1,𝔽8) ⋊ D13
HallC72×C13 ⋊ C3×D5
HallC5×C72 ⋊ C3×D13
HallC7×ΓL(1,𝔽8) ⋊ D65
HallC5×C13 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×D65
SylowC13 ⋊ ΓL(1,𝔽8)×D35
SylowC5 ⋊ ΓL(1,𝔽8)×D91

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1145 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D455, (ΓL(1,𝔽8)⋊D13)⋊D35, (ΓL(1,𝔽8)⋊D7)⋊D65, …
maximal normal subgroup ofAGL(1,𝔽7)×D455, (ΓL(1,𝔽8)⋊D13)⋊D35, (ΓL(1,𝔽8)⋊D7)⋊D65, …
maximal quotient ofΓL(1,𝔽8)×Dic455, C2×ΓL(1,𝔽8)×D455

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 164);