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#14559027⋊C5 #27130696

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

Aliases

unambiguous semidirect product#14559027⋊C5

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C3×C5
Hall#11925881⋊C5 ⋊ C2
HallD13×ΓL(1,𝔽32) ⋊ C3
Hall#14559027 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C3
Hall#11925881 ⋊ C2×C5
HallD13×C31 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ D13⋊C3
SylowC31 ⋊ C5×D13⋊C3
HallD13 ⋊ (C31⋊C3)⋊C5
SylowC13 ⋊ C2×(C31⋊C3)⋊C5

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|d^a=d^12,d^b=d^3,e^b=e^5,e^c=e^16

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#18012823⋊C5, #18012825⋊C5, (#14559023⋊C2)⋊C5, …
maximal normal subgroup of#18012823⋊C5, #18012825⋊C5, (#14559023⋊C2)⋊C5, …
maximal quotient of#18012816⋊C5, C2×#14559027⋊C5, #20299826⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 68);