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C4×#4485 #10686128

order768
isoclinismisoclinic class of #4451
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#4485

Splittings

FittingC3×C4×C4⋊C8 ⋊ C2
SylowC3 ⋊ C4×#331

Subgroups

subgroupG/H
centerC22×C4(C2×D3)⋊C4
commutatorC2×C3×C4C2×C42
FrattiniC2×C42C22×D3
FittingC3×C4×C4⋊C8C2
socleC23×C3C2×C22⋊C4
prime radicalC2×#874C22
cosocleC2×C3×C42C23
hypercenterC4×C4⋊C8D3
hypocenterC3C4×#331
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 60509);