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C2×C5×C3⋊(C3⋊C8) #10623887

order720
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊(C3⋊C8)
unambiguous semidirect product(C2×C3)⋊(C5×C3⋊C8)

Splittings

derived, SylowC32 ⋊ C2×C5×C8
HallC32×C5 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5C3⋊D3
commutator, hypocenterC32C2×C5×C8
FrattiniC4C2×C5×C3⋊D3
FittingC2×C32×C4×C5C2
socle, prime radicalC22×C32×C5C4
cosocleC32×C4C22×C5
LCSG ▷ C32
UCSC1 ◁ C2×C4×C5

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 720

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×C3⋊(C3⋊C8), #13084719, #13084720, …
maximal normal subgroup ofDic5×C3⋊(C3⋊C8), #13084719, #13084720, …
maximal quotient ofC4×C5×C3⋊(C3⋊C8), C5×C4⋊(C3⋊(C3⋊C8)), C2×C5×C3⋊(C3⋊C16), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 356);