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D3×#2170 #10948411

order768
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productD3×#2170

Splittings

FittingC3×#2170 ⋊ C2
SylowC3 ⋊ C2×#2170

Subgroups

subgroupG/H
centerC16D3×D4
commutatorC3×C4C23×C8
FrattiniC2×C8C23×D3
FittingC3×#2170C2
socleC2×C3C2×C8×D4
prime radicalD3×#135C4
cosocleC2×C3×C8C24
hypercenter#2170D3
hypocenterC3C2×#2170
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C16 ◁ C2×C16 ◁ #2170

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#12046, D3×#33443, D3×#12047, …
maximal normal subgroup ofD3×#12046, D3×#33443, D3×#12047, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322792);