Finite Group Databasebeta

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#106×GO+(4,𝔽2) #72269015

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#106×GO+(4,𝔽2)

Splittings

FittingC32×#106 ⋊ D4
SylowC32 ⋊ D4×#106

Subgroups

subgroupG/H
centerC22D4×GO+(4,𝔽2)
commutatorC4×C3⋊D3C23×C4
FrattiniC2×C4C22×GO+(4,𝔽2)
FittingC32×#106D4
socleC22×C32D42
prime radicalC22×GO+(4,𝔽2)D4
cosocleC2×C4×C3⋊D3C24
hypercenter#106GO+(4,𝔽2)
hypocenterC32D4×#106
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

1726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.