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C7×C11×C13×C3⋊D3 #31825084

order18018
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC7×C11×C13×C3⋊D3
unambiguous semidirect productC3⋊(D3×C7×C11×C13)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C2
derived, SylowC32 ⋊ C2×C7×C11×C13
HallC32×C11×C13 ⋊ C2×C7
HallC32×C7×C13 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C13
HallC32×C13 ⋊ C2×C7×C11
HallC32×C11 ⋊ C2×C7×C13
HallC32×C7 ⋊ C2×C11×C13

Subgroups

subgroupG/H
center, hypercenterC7×C11×C13C3⋊D3
commutator, cosocle, hypocenterC32C2×C7×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C32
UCSC1 ◁ C7×C11×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×C13×#157, C7×C11×#90865, C7×C13×C11⋊#157, …
maximal normal subgroup ofC7×C11×C13×#157, C7×C11×#90865, C7×C13×C11⋊#157, …
maximal quotient ofC7×C11×C13×C3⋊Dic3, C2×C7×C11×C13×C3⋊D3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 129);