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#14559030⋊C5 #27130699

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

Aliases

unambiguous semidirect product#14559030⋊C5

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C3×C5
Hall#11925882⋊C5 ⋊ C2
HallC13⋊(D31⋊C5) ⋊ C3
Hall#14559030 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C3
Hall#11925882 ⋊ C2×C5
HallD403 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ D13⋊C3
SylowC31 ⋊ C5×D13⋊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|d^a=d^12,e^a=e^30,d^b=d^3,e^b=e^25,e^c=e^16

Conjugacy classes & character table

53 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#14559022⋊C2)⋊C5, C2×#14559030⋊C5, (C13⋊C3)⋊AGL(1,𝔽31), …
maximal normal subgroup of(#14559022⋊C2)⋊C5, C2×#14559030⋊C5, (C13⋊C3)⋊AGL(1,𝔽31), …
maximal quotient of#18012819⋊C5, C2×#14559030⋊C5, #20299829⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 71);