Finite Group Databasebeta

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C4×#4989 #10716352

order768
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4×#4989

Splittings

FittingC2×C3×C4×C4⋊C4 ⋊ C2
SylowC3 ⋊ C4×#385

Subgroups

subgroupG/H
centerC23×C4C22×D3
commutatorC22×C3C22×C42
FrattiniC24C23×D3
FittingC2×C3×C4×C4⋊C4C2
socle, cosocleC24×C3C24
prime radicalC24×D3C23
hypercenterC2×C4×C4⋊C4D3
hypocenterC3C4×#385
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 90733);