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C3×Dic181⋊C5 #24925796

order10860
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic181⋊C5
unambiguous semidirect product(C3×Dic181)⋊C5

Splittings

derived, SylowC181 ⋊ C3×C4×C5
HallC3×C181⋊C5 ⋊ C4
HallC3×Dic181 ⋊ C5
HallC181⋊C5 ⋊ C3×C4
HallDic181 ⋊ C3×C5
HallC3×C181 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D181⋊C5
commutator, hypocenterC181C3×C4×C5
FrattiniC2C3×D181⋊C5
Fitting, socleC2×C3×C181C2×C5
prime radicalC2×C3×C181⋊C5C2
cosocleC2×C181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×Dic181⋊C5, #20266765⋊C5, C3×(Dic181⋊C3)⋊C5, …
maximal normal subgroup ofC9×Dic181⋊C5, #20266765⋊C5, C3×(Dic181⋊C3)⋊C5, …
maximal quotient ofC9×Dic181⋊C5, C32×Dic181⋊C5, C3×C3⋊(Dic181⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 12);