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#14559023⋊C5 #27130692

order12090
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#14559023⋊C5

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C3×C5
Hall#11925881⋊C5 ⋊ C2
HallC13×D31⋊C5 ⋊ C3
Hall#14559023 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C3
Hall#11925881 ⋊ C2×C5
HallC13×D31 ⋊ C3×C5
HallD31⋊C5 ⋊ C13⋊C3
HallΓL(1,𝔽32) ⋊ C2×C13⋊C3
HallD31 ⋊ C5×C13⋊C3
SylowC31 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,13,31|e^a=e^30,d^b=d^3,e^b=e^5,e^c=e^16

Conjugacy classes & character table

83 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#14559023⋊C2)⋊C5, C2×#14559023⋊C5, C13⋊C3×AGL(1,𝔽31), …
maximal normal subgroup of(#14559023⋊C2)⋊C5, C2×#14559023⋊C5, C13⋊C3×AGL(1,𝔽31), …
maximal quotient of#18012812⋊C5, C2×#14559023⋊C5, #20299822⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 64);