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C22×C5×C13×C13⋊C3 #23778602

order10140
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C13×C13⋊C3

Splittings

Fitting, socle, HallC22×C5×C132 ⋊ C3
derivedC13 ⋊ C22×C3×C5×C13
HallC5×C132 ⋊ C22×C3
HallC22×C132 ⋊ C3×C5
SylowC132 ⋊ C22×C3×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5×C13C13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C5×C13
FrattiniC1G
Fitting, socleC22×C5×C132C3
LCSG ▷ C13
UCSC1 ◁ C22×C5×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1820 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×A4×C13×C13⋊C3, C5×C13⋊C3×C22⋊(C13⋊C3), C22×C5×C13⋊C32, …
maximal normal subgroup ofC5×A4×C13×C13⋊C3, C5×C13⋊C3×C22⋊(C13⋊C3), C22×C5×C13⋊C32, …
maximal quotient ofC22×C5×C13×C13⋊C9, C2×C5×D3×C13×C13⋊C3, C22×C3×C5×C13×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 260);