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C22×C5×C7×C13⋊C3 #19129871

order5460
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C7×C13⋊C3

Splittings

Fitting, socle, HallC22×C5×C7×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C5×C7
HallC5×C7×C13 ⋊ C22×C3
HallC22×C7×C13 ⋊ C3×C5
HallC22×C5×C13 ⋊ C3×C7
HallC7×C13 ⋊ C22×C3×C5
HallC5×C13 ⋊ C22×C3×C7
HallC22×C13 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C5×C7C13⋊C3
commutator, hypocenterC13C22×C3×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C5×ΓL(1,𝔽8)×C13⋊C3, C5×C7×A4×C13⋊C3, C5×C13⋊C3×C22⋊ΓL(1,𝔽8), …
maximal normal subgroup ofC22×C5×ΓL(1,𝔽8)×C13⋊C3, C5×C7×A4×C13⋊C3, C5×C13⋊C3×C22⋊ΓL(1,𝔽8), …
maximal quotient ofC22×C5×C7×C13⋊C9, C2×C5×D3×C7×C13⋊C3, C22×C3×C5×C7×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 213);