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C5×#14559023 #27130664

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

Aliases

direct productC5×#14559023

Splittings

Fitting, socle, HallC5×C13×C31 ⋊ C2×C3
derived, HallC13×C31 ⋊ C2×C3×C5
HallC5×#11925881 ⋊ C2
HallC5×C13×D31 ⋊ C3
Hall#11925881 ⋊ C2×C5
HallC13×D31 ⋊ C3×C5
HallC5×D31 ⋊ C13⋊C3
HallC5×C31 ⋊ C2×C13⋊C3
HallC5×C13 ⋊ D31⋊C3
HallD31 ⋊ C5×C13⋊C3
SylowC31 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#14559023
commutator, cosocle, hypocenterC13×C31C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C31C2×C3
LCSG ▷ C13×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

395 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#14559023⋊C2, #14559023⋊D5, D5×#14559023, …
maximal normal subgroup ofC5×#14559023⋊C2, #14559023⋊D5, D5×#14559023, …
maximal quotient ofC5×#18012812, C2×C5×#14559023, C5×#20299822, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 36);