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C2×C11×ΓL(1,𝔽8)×D13 #26046521

order12012
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×ΓL(1,𝔽8)×D13

Splittings

Fitting, socleC2×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C11
HallC2×C7×C11×D13 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C22
HallC7×C11×C13 ⋊ C22×C3
HallC2×C7×D13 ⋊ C3×C11
HallC13×ΓL(1,𝔽8) ⋊ C22×C11
HallC11×C13 ⋊ C22×ΓL(1,𝔽8)
HallC7×C11 ⋊ C2×C3×D13
SylowC13 ⋊ C22×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C11×D13

Subgroups

subgroupG/H
center, hypercenterC2×C11ΓL(1,𝔽8)×D13
commutator, cosocle, hypocenterC7×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

880 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11×ΓL(1,𝔽8)×D13⋊C3, D3×C11×ΓL(1,𝔽8)×D13, C2×C3×C11×ΓL(1,𝔽8)×D13, …
maximal normal subgroup ofC2×C11×ΓL(1,𝔽8)×D13⋊C3, C2×C3×C11×ΓL(1,𝔽8)×D13
maximal quotient ofC2×C11×D13×C7⋊C9, D3×C11×ΓL(1,𝔽8)×D13, C2×C3×C11×ΓL(1,𝔽8)×D13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 111);