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D3×#4070 #11754347

order960
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD3×#4070

Splittings

HallC3×C5 ⋊ C2×C22⋊Q8
SylowC5 ⋊ D3×C22⋊Q8
SylowC3 ⋊ C2×#4070

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
prime radicalC23×C5×D3C22
hypercenterC22×C4D3×D5
hypocenterC3×C5C2×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#64672, D3×#64687, #14283170, …
maximal normal subgroup ofD3×#64672, D3×#64687, #14283170, …
maximal quotient ofD3×#65501, D3×#65499, D3×#65222, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 8542);