Finite Group Databasebeta

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C4×#88421 #13137221

order1728
isoclinismisoclinic class of #88421
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×#88421

Splittings

SylowC3×C9 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2×C4#6194
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC3×C42×C9C22
socleC22×C32C2×#67
prime radicalC2×#88421C2
cosocleC2×C3×C4×C9C23
hypercenterC42D3×D9
hypocenterC3×C9C4×D8
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C42

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 3284);