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D3×#887 #10594356

order576
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD3×#887

Splittings

SylowC32 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
center, FrattiniC22C22×D32
commutatorC2×C32C23×C4
FittingC32×C4⋊C4C22
socle, cosocleC22×C32C24
prime radicalC22×C3×D3C23
hypercenterC4⋊C4D32
hypocenterC32C2×C4×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

631 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4852, D3×#4758, D3×#4790, …
maximal normal subgroup ofD3×#4852, D3×#4758, D3×#4790, …
maximal quotient ofD3×#4649, D3×Dic3×C4⋊C4, #11800841, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 6238);