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C5×C3⋊#11715871 #26040705

order11580
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#11715871
unambiguous semidirect productC3⋊(C5×#11715871)

Splittings

Fitting, socle, HallC3×C5×C193 ⋊ C4
derived, HallC3×C193 ⋊ C4×C5
HallC5×C193 ⋊ Dic3
SylowC193 ⋊ C5×Dic3
HallC3×C5 ⋊ #11715871
SylowC3 ⋊ C5×#11715871

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#11715871
commutator, hypocenterC3×C193C4×C5
FrattiniC1G
Fitting, socleC3×C5×C193C4
prime radicalC3×C5×D193C2
cosocleC3×D193C2×C5
LCSG ▷ C3×C193
UCSC1 ◁ C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

750 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊#11715871, C5×C3⋊(#11715871⋊C3), C3×C5×C3⋊#11715871, …
maximal normal subgroup ofC5×C3⋊(#11715871⋊C3), C3×C5×C3⋊#11715871
maximal quotient ofC5×C9⋊#11715871, C3×C5×C3⋊#11715871, C5×C3⋊(C3⋊#11715871)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11580, 31);