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D7×D11×C13⋊C3 #26046503

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

Aliases

direct productD7×D11×C13⋊C3

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C22×C3
HallC13×D7×D11 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ C22
HallC11×C13⋊C3 ⋊ C2×D7
HallC7×C13⋊C3 ⋊ C2×D11
HallC11×C13 ⋊ C2×C3×D7
HallC7×C13 ⋊ C2×C3×D11
HallC7×C11 ⋊ C22×C13⋊C3
SylowC13 ⋊ C3×D7×D11
SylowC11 ⋊ C2×D7×C13⋊C3
SylowC7 ⋊ C2×D11×C13⋊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

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C13⋊C3×AGL(1,𝔽7), C3×D7×D11×C13⋊C3, D11×C13⋊C3×D21, …
maximal normal subgroup ofD11×C13⋊C3×AGL(1,𝔽7), C3×D7×D11×C13⋊C3
maximal quotient ofD7×D11×C13⋊C9, C3×D7×D11×C13⋊C3, D11×C13⋊C3×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 93);