Finite Group Databasebeta

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C2×C3×#6763 #13089148

order1440
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C3×#6763
unambiguous semidirect productD5⋊(C3×#217)

Splittings

FittingC23×C32×C5 ⋊ C4
HallC32×C5 ⋊ C2×C22⋊C4
SylowC32 ⋊ C2×C22⋊AGL(1,𝔽5)
SylowC5 ⋊ C2×C3×#217

Subgroups

subgroupG/H
centerC22×C3C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C22×C3×C4
FrattiniC2C22×C3×ΓL(1,𝔽16)
FittingC23×C32×C5C4
socleC22×C32×C5C2×C4
prime radicalC23×C32×D5C2
cosocleC2×C3×D5C23×C3
hypercenterC23×C3ΓL(1,𝔽16)
hypocenterC3×C5C2×C3×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C23×C3

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×#67, C2×#67⋊ΓL(1,𝔽16), C3×#11756871, …
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×#67, C2×#67⋊ΓL(1,𝔽16), C3×#11756871, …
maximal quotient ofC3×#11752459, C3×D5⋊#834, C3×#11752426, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5465);