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C32×C11×C13×D7 #31825096

order18018
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C2×C32×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×C13×D7

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C2
derived, SylowC7 ⋊ C2×C32×C11×C13
HallC7×C11×C13 ⋊ C2×C32
HallC32×C7×C13 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C13
HallC7×C13 ⋊ C2×C32×C11
HallC7×C11 ⋊ C2×C32×C13
HallC32×C7 ⋊ C2×C11×C13

Subgroups

subgroupG/H
center, hypercenterC32×C11×C13D7
commutator, cosocle, hypocenterC7C2×C32×C11×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C2
LCSG ▷ C7
UCSC1 ◁ C32×C11×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

6435 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C11×D7×D13, C32×C13×D7×D11, C32×D7×D143, …
maximal normal subgroup ofC32×C11×D7×D13, C32×C13×D7×D11, C32×D7×D143, …
maximal quotient ofC32×C11×C13×Dic7, C2×C32×C11×C13×D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18018, 141);