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D11×#10587717 #26046493

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

Aliases

direct productD11×#10587717

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallC7×D11×D13 ⋊ C3
HallC11×#63271 ⋊ C22
HallD11×D13 ⋊ ΓL(1,𝔽8)
Hall#63271 ⋊ C2×D11
HallC11×C13 ⋊ C22×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×#10587717
SylowC7 ⋊ D11×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C22×C3
LCSG ▷ C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×D11×D13⋊C3, C3×D11×#10587717, D33×#10587717, …
maximal normal subgroup ofΓL(1,𝔽8)×D11×D13⋊C3, C3×D11×#10587717
maximal quotient ofD11×#13109897, C3×D11×#10587717, D33×#10587717, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 83);