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C22×C13⋊C3×C43 #20269488

order6708
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C43 · Schur multiplier (H2) = C2

Aliases

direct productC22×C13⋊C3×C43

Splittings

Fitting, socle, HallC22×C13×C43 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C43
HallC13×C43 ⋊ C22×C3
HallC22×C13 ⋊ C3×C43

Subgroups

subgroupG/H
center, hypercenterC22×C43C13⋊C3
commutator, hypocenterC13C22×C3×C43
FrattiniC1G
Fitting, socleC22×C13×C43C3
LCSG ▷ C13
UCSC1 ◁ C22×C43

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C13⋊C3×C43, C13⋊C3×C22⋊(C43⋊C3), C22×C13⋊C3×C43⋊C3, …
maximal normal subgroup ofA4×C13⋊C3×C43, C13⋊C3×C22⋊(C43⋊C3), C22×C13⋊C3×C43⋊C3, …
maximal quotient ofC22×C43×C13⋊C9, C2×D3×C13⋊C3×C43, C22×C3×C13⋊C3×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6708, 68);