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Dic3×(C181⋊C3)⋊C5 #45656405

order32580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productDic3×(C181⋊C3)⋊C5
unambiguous semidirect productC3⋊(C4×(C181⋊C3)⋊C5)
unambiguous semidirect product(Dic3×C181⋊C3)⋊C5
unambiguous semidirect product(Dic3×C181⋊C5)⋊C3

Splittings

derivedC3×C181 ⋊ C3×C4×C5
HallC3×(C181⋊C3)⋊C5 ⋊ C4
HallDic3×C181⋊C3 ⋊ C5
HallC3×C181⋊C3 ⋊ C4×C5
HallC181⋊C5 ⋊ C3×Dic3
SylowC181 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D3×(C181⋊C3)⋊C5
commutator, hypocenterC3×C181C3×C4×C5
Fitting, socle, cosocleC2×C3×C181C2×C3×C5
prime radicalC2×C3×(C181⋊C3)⋊C5C2
LCSG ▷ C3×C181
UCSC1 ◁ C2

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 76);