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C4×C5×#63271 #19129663

order5460
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#63271

Splittings

Fitting, HallC4×C5×C7×C13 ⋊ C3
derived, HallC7×C13 ⋊ C3×C4×C5
HallC5×C7×C13 ⋊ C3×C4
HallC4×C7×C13 ⋊ C3×C5
HallC4×C5×C13 ⋊ ΓL(1,𝔽8)
HallC4×C5×C7 ⋊ C13⋊C3
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
HallC4×C13 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C13⋊C3
HallC4×C7 ⋊ C5×C13⋊C3
SylowC13 ⋊ C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5#63271
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC2C2×C5×#63271
FittingC4×C5×C7×C13C3
socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×ΓL(1,𝔽8)×C13⋊C3, C5×Dic3×#63271, C3×C4×C5×#63271, …
maximal normal subgroup ofC4×C5×ΓL(1,𝔽8)×C13⋊C3, C3×C4×C5×#63271, C4×C25×#63271, …
maximal quotient ofC4×C5×#11717942, C5×Dic3×#63271, C3×C4×C5×#63271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 5);