Finite Group Databasebeta

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C4×#4981 #10717023

order768
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#4981

Splittings

SylowC3 ⋊ C4×#398

Subgroups

subgroupG/H
centerC23×C4C22×D3
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×C4×C4⋊C4C2
socle, prime radical, cosocleC24×C3C24
hypercenterC2×C4×C4⋊C4D3
hypocenterC3C4×#398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 768

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 91404);