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C5×ΓL(1,𝔽8)×D77 #30633542

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D77

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC72×C11 ⋊ C2×C3×C5
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×D77 ⋊ C3
HallC7×C11×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×D77 ⋊ C3×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ D11
HallC5×C72 ⋊ C3×D11
HallC7×ΓL(1,𝔽8) ⋊ C5×D11
HallC5×C11 ⋊ D7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×C5×D11
SylowC11 ⋊ C5×D7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D77
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C72×C11
UCSC1 ◁ C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

1000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D77, C5×(ΓL(1,𝔽8)⋊D7)⋊D11, C5×D7×ΓL(1,𝔽8)×D11, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D77, C5×(ΓL(1,𝔽8)⋊D7)⋊D11, C5×D7×ΓL(1,𝔽8)×D11, …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic77, C2×C5×ΓL(1,𝔽8)×D77

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 87);