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C4×#5245 #10801083

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#5245

Splittings

FittingC3×C4×2−1+4 ⋊ C2
SylowC3 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#953
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×C4×2−1+4C2
socleC22×C3C2×#120
prime radicalC2×#5245C2
cosocleC22×C3×C4C24
hypercenterC4×2−1+4D3
hypocenterC3C4×#454
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×2−1+4

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 175464);