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D3×#2115 #10947874

order768
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD3×#2115

Splittings

FittingC3×#2115 ⋊ C2
SylowC3 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC8D3×C22⋊C4
commutatorC22×C3C23×C8
FrattiniC2×C8C23×D3
FittingC3×#2115C2
socleC2×C3C22×C22⋊C8
prime radicalC2×D3×#41C4
cosocleC2×C3×C8C24
hypercenter#2115D3
hypocenterC3C2×#2115
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2115

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#33426, D3×#12741, D3×#12874, …
maximal normal subgroup ofD3×#33426, D3×#12741, D3×#12874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 322255);