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D3×#2128 #10947973

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42

Aliases

direct productD3×#2128

Splittings

FittingC3×#2128 ⋊ C2
SylowC3 ⋊ C2×#2128

Subgroups

subgroupG/H
centerC2C2×D3×#99
commutatorC2×C3×C4C23×C4
FrattiniC2×D4C23×D3
FittingC3×#2128C2
socleC2×C3C22×#99
prime radicalD3×#535C2
cosocleC2×C3×D4C24
hypercenter#2128D3
hypocenterC3C2×#2128
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #2128

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#12711, D3×#33553, D3×#12778, …
maximal normal subgroup ofD3×#12711, D3×#33553, D3×#12778, …
maximal quotient ofC2×D3×#2128, D3×#12583, #72270460, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322354);