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C22×C13⋊C3×C41 #20264202

order6396
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2

Aliases

direct productC22×C13⋊C3×C41

Splittings

Fitting, socle, HallC22×C13×C41 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C41
HallC13×C41 ⋊ C22×C3
HallC22×C13 ⋊ C3×C41

Subgroups

subgroupG/H
center, hypercenterC22×C41C13⋊C3
commutator, hypocenterC13C22×C3×C41
FrattiniC1G
Fitting, socleC22×C13×C41C3
LCSG ▷ C13
UCSC1 ◁ C22×C41

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C13⋊C3×C41, C2×D3×C13⋊C3×C41, C22×C3×C13⋊C3×C41, …
maximal normal subgroup ofA4×C13⋊C3×C41, C22×C3×C13⋊C3×C41, C22×C13⋊C3×C41⋊C5, …
maximal quotient ofC22×C41×C13⋊C9, C2×D3×C13⋊C3×C41, C22×C3×C13⋊C3×C41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 43);