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C5⋊#14559022 #27130679

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

Aliases

unambiguous semidirect productC5⋊#14559022

Splittings

Fitting, socle, derived, HallC5×C13×C31 ⋊ C2×C3
HallC5×#11925882 ⋊ C2
HallC13×D155 ⋊ C3
Hall#11925882 ⋊ D5
HallC13×C31 ⋊ C3×D5
HallD155 ⋊ C13⋊C3
HallC5×C31 ⋊ C2×C13⋊C3
HallC5×C13 ⋊ D31⋊C3
SylowC31 ⋊ D5×C13⋊C3
SylowC13 ⋊ C5⋊(D31⋊C3)
SylowC5 ⋊ #14559022

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C31C2×C3
LCSG ▷ C5×C13×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,13,31|c^a=c^4,e^a=e^30,d^b=d^3,e^b=e^25

Conjugacy classes & character table

353 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14559026⋊D5, #14559030⋊D5, D5×#14559022, …
maximal normal subgroup of#14559026⋊D5, #14559030⋊D5, D5×#14559022, …
maximal quotient of#37563752, C2×C5⋊#14559022, C5⋊#20299821, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 51);