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C3×#10599498 #14302882

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10599498

Splittings

FittingC3×C5×H(3,ℤ/4) ⋊ C2
HallC3×C5 ⋊ #1911
SylowC5 ⋊ C3×#1911

Subgroups

subgroupG/H
centerC2×C3#64954
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC3×C5×H(3,ℤ/4)C2
socleC2×C3×C5#386
prime radicalC3×#65859C2
cosocleC22×C4×C5C23×C3
hypercenterC3×H(3,ℤ/4)D5
hypocenterC5C3×#1911
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×H(3,ℤ/4)

724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28580);