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C2×C3×#64697 #14313562

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×#64697

Splittings

FittingC2×C3×C5×#101 ⋊ C2
HallC3×C5 ⋊ C2×#355
SylowC5 ⋊ C2×C3×#355

Subgroups

subgroupG/H
centerC22×C3#3938
commutatorC2×C4×C5C22×C3×C4
FrattiniC2×Q8C22×C3×D5
FittingC2×C3×C5×#101C2
socleC22×C3×C5#99
prime radicalC22×C3×D20C4
cosocleC2×C5×Q8C23×C3
hypercenterC2×C3×#101D5
hypocenterC5C2×C3×#355
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×Q8 ◁ C2×C3×#101

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39260);