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C5×C13⋊C3×#261 #23778446

order10140
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×#261

Splittings

Fitting, socle, HallC5×C132 ⋊ C3×C4
derived, SylowC132 ⋊ C3×C4×C5
HallC5×C13×#261 ⋊ C3
HallC5×C13×C13⋊C3 ⋊ C4
HallC13×#261 ⋊ C3×C5
HallC13×C13⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×#261
commutator, hypocenterC132C3×C4×C5
FrattiniC1G
Fitting, socleC5×C132C3×C4
prime radicalC5×D13×C13⋊C3C2
cosocleC13×D13C2×C3×C5
LCSG ▷ C132
UCSC1 ◁ C5

50 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×AGL(1,𝔽13), C3×C5×C13⋊C3×#261, C5×C13⋊C3×C3⋊#261
maximal normal subgroup ofC5×C13⋊C3×AGL(1,𝔽13), C3×C5×C13⋊C3×#261
maximal quotient ofC5×#261×C13⋊C9, C3×C5×C13⋊C3×#261, C5×C13⋊C3×C3⋊#261

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 104);