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D3×D5×C22⋊C4 #11753198

order960
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×D5×C22⋊C4

Splittings

FittingC3×C5×C22⋊C4 ⋊ C22
HallC3×C5 ⋊ C22×C22⋊C4
SylowC5 ⋊ C2×D3×C22⋊C4
SylowC3 ⋊ C2×D5×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×D5
commutatorC2×C3×C5C23×C4
FittingC3×C5×C22⋊C4C22
socle, cosocleC22×C3×C5C24
prime radicalC23×D3×D5C2
hypercenterC22⋊C4D3×D5
hypocenterC3×C5C22×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

1348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#64866, D3×C22⋊C4×AGL(1,𝔽5), #14319659, …
maximal normal subgroup ofD3×#64866, D3×C22⋊C4×AGL(1,𝔽5), #14319659, …
maximal quotient ofD3×D5×#95, D5×#4666, #14319390, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 7393);