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C5×#11763985 #19129709

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

Aliases

direct productC5×#11763985

Splittings

Fitting, socle, HallC5×C7×C13 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C5
HallC5×C7⋊#261 ⋊ C3
HallC5×#63270 ⋊ C4
HallC7⋊#261 ⋊ C3×C5
Hall#63270 ⋊ C4×C5
HallC5×C13 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ AGL(1,𝔽13)
SylowC13 ⋊ C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C5×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC5#11763985
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC1G
Fitting, socleC5×C7×C13C3×C4
LCSG ▷ C7×C13
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)⋊AGL(1,𝔽13), C3×C5×#11763985, C5×C3⋊#11763985, …
maximal normal subgroup ofC5×ΓL(1,𝔽8)⋊AGL(1,𝔽13), C3×C5×#11763985, C25×#11763985, …
maximal quotient ofC5×#15692592, C3×C5×#11763985, C5×C3⋊#11763985, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 51);