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Dic5×H(3,ℤ/4) #12004463

order1280
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productDic5×H(3,ℤ/4)

Splittings

SylowC5 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C42×D5
commutatorC4×C5C43
FrattiniC23×C4C22×D5
FittingC2×C5×H(3,ℤ/4)C2
socleC22×C5C2×#95
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×H(3,ℤ/4)D5
hypocenterC5C4×H(3,ℤ/4)
LCSG ▷ C4×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 74731);