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C2×D5×#63270 #19129807

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×#63270
unambiguous semidirect productC5⋊(C22×#63270)
unambiguous semidirect product(C2×C5)⋊(C2×#63270)

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC5×C7×C13 ⋊ C22×C3
HallC2×C7×D5×C13 ⋊ C3
HallC5×#63270 ⋊ C22
HallC2×D5×C13 ⋊ ΓL(1,𝔽8)
HallC2×C7×D5 ⋊ C13⋊C3
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C22×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C2×D5×C13⋊C3
SylowC5 ⋊ C22×#63270

Subgroups

subgroupG/H
center, hypercenterC2D5×#63270
commutator, hypocenterC5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D5×ΓL(1,𝔽8)×C13⋊C3, D3×D5×#63270, C2×C3×D5×#63270, …
maximal normal subgroup ofC2×D5×ΓL(1,𝔽8)×C13⋊C3, C2×C3×D5×#63270, C2×C5×D5×#63270, …
maximal quotient ofC2×D5×#11717941, D3×D5×#63270, C2×C3×D5×#63270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 149);