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C5×#11763958 #19129682

order5460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#11763958

Splittings

derived, HallC7×C13 ⋊ C3×C4×C5
HallC5×C7×Dic13 ⋊ C3
HallC5×#63271 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC7×Dic13 ⋊ C3×C5
Hall#63271 ⋊ C4×C5
HallC5×Dic13 ⋊ ΓL(1,𝔽8)
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
HallDic13 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ Dic13⋊C3
SylowC13 ⋊ C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C5×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#10587717
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC2C5×#10587717
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)×Dic13⋊C3, C3×C5×#11763958, C5×C3⋊#11763958, …
maximal normal subgroup ofC5×ΓL(1,𝔽8)×Dic13⋊C3, C3×C5×#11763958, C25×#11763958, …
maximal quotient ofC5×#15692566, C3×C5×#11763958, C5×C3⋊#11763958, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 24);