Finite Group Databasebeta

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C3×C11×C13×D21 #31825088

order18018
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C13 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C2
derivedC3×C7 ⋊ C2×C3×C11×C13
HallC32×C11×C13 ⋊ D7
HallC7×C11×C13 ⋊ C3×D3
HallC32×C7×C13 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C13
HallC32×C13 ⋊ C11×D7
HallC32×C11 ⋊ C13×D7
HallC7×C13 ⋊ C3×D3×C11
HallC7×C11 ⋊ C3×D3×C13
HallC32×C7 ⋊ C2×C11×C13
SylowC32 ⋊ C11×C13×D7
SylowC7 ⋊ C3×D3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13D21
commutator, cosocle, hypocenterC3×C7C2×C3×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C3×C7
UCSC1 ◁ C3×C11×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

5148 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×D13×D21, C3×C13×D11×D21, C3×D21×D143, …
maximal normal subgroup ofC3×C11×D13×D21, C3×C13×D11×D21, C3×D21×D143, …
maximal quotient ofC3×C11×C13×Dic21, C2×C3×C11×C13×D21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 133);