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C2×C5×D3×M16 #11756128

order960
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×D3×M16

Splittings

FittingC2×C3×C5×M16 ⋊ C2
HallC3×C5 ⋊ C22×M16
SylowC3 ⋊ C22×C5×M16

Subgroups

subgroupG/H
centerC2×C4×C5C22×D3
commutatorC2×C3C23×C4×C5
FrattiniC4C23×C5×D3
FittingC2×C3×C5×M16C2
socleC22×C3×C5C22×C4
prime radicalC23×C5×D3C4
cosocleC3×C4C24×C5
hypercenterC2×C5×M16D3
hypocenterC3C22×C5×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×M16

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×H(3,ℤ/4), D3×#64777, C5×D3×#338, …
maximal normal subgroup ofC5×D3×H(3,ℤ/4), D3×#64777, C5×D3×#338, …
maximal quotient ofC2×C5×D3×#97, C4×C5×D3×M16, C2×C5×Dic3×M16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10323);