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C13⋊C3×C7⋊AGL(1,𝔽5) #19129751

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

Aliases

direct productC13⋊C3×C7⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C3×C4
HallC13×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C4
HallC7×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C13⋊C3 ⋊ Dic7
HallC7×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×Dic7
HallC5×C7 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ AGL(1,𝔽5)×C13⋊C3
SylowC5 ⋊ Dic7×C13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C3×C4
LCSG ▷ C5×C7×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13⋊C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C13⋊C3×C7⋊AGL(1,𝔽5), C13⋊C3×C3⋊(C7⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC13⋊C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C13⋊C3×C7⋊AGL(1,𝔽5), C5×C13⋊C3×C7⋊AGL(1,𝔽5), …
maximal quotient ofC13⋊C9×C7⋊AGL(1,𝔽5), C3×C13⋊C3×C7⋊AGL(1,𝔽5), C13⋊C3×C3⋊(C7⋊AGL(1,𝔽5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 93);