Finite Group Databasebeta

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C11×C13⋊C3×D21 #31825070

order18018
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13⋊C3×D21
unambiguous semidirect productC3⋊(C11×D7×C13⋊C3)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C2×C3
derivedC3×C7×C13 ⋊ C2×C3×C11
HallC3×C7×C11×C13⋊C3 ⋊ C2
HallC3×C11×C13⋊C3 ⋊ D7
HallC7×C11×C13 ⋊ C3×D3
HallC3×C7×C13⋊C3 ⋊ C2×C11
HallC11×C13 ⋊ C3×D21
HallC3×C13⋊C3 ⋊ C11×D7
HallC7×C13 ⋊ C3×D3×C11
HallC7×C11 ⋊ D3×C13⋊C3
SylowC13 ⋊ C3×C11×D21
SylowC7 ⋊ D3×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C13⋊C3×D21
commutator, cosocle, hypocenterC3×C7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×D21×D13⋊C3, D21×C11⋊(D13⋊C3), D11×C13⋊C3×D21, …
maximal normal subgroup ofC11×D21×D13⋊C3, D21×C11⋊(D13⋊C3), D11×C13⋊C3×D21, …
maximal quotient ofC11×C13⋊C3×Dic21, C2×C11×C13⋊C3×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 115);