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C22×C5×#63270 #19129873

order5460
isoclinismisoclinic class of #63270
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×#63270

Splittings

Fitting, socle, HallC22×C5×C7×C13 ⋊ C3
derived, HallC7×C13 ⋊ C22×C3×C5
HallC5×C7×C13 ⋊ C22×C3
HallC22×C7×C13 ⋊ C3×C5
HallC22×C5×C13 ⋊ ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C13⋊C3
HallC5×C13 ⋊ C22×ΓL(1,𝔽8)
HallC22×C13 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22×C13⋊C3
HallC22×C7 ⋊ C5×C13⋊C3
SylowC13 ⋊ C22×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C5#63270
commutator, hypocenterC7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C5×ΓL(1,𝔽8)×C13⋊C3, C5×A4×#63270, C5×#63270⋊A4, …
maximal normal subgroup ofC22×C5×ΓL(1,𝔽8)×C13⋊C3, C5×A4×#63270, C5×#63270⋊A4, …
maximal quotient ofC22×C5×#11717941, C2×C5×D3×#63270, C22×C3×C5×#63270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 215);