Finite Group Databasebeta

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C4⋊C4×Dic3⋊C4 #10716624

order768
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×Dic3⋊C4

Splittings

SylowC3 ⋊ C4⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D3
commutatorC22×C3C22×C42
FittingC2×C3×C4×C4⋊C4C2
socle, prime radical, cosocleC24×C3C24
hypercenterC2×C4×C4⋊C4D3
hypocenterC3C4⋊C42
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 768

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 91005);