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C2×C5×#5088 #14437644

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C5×#5088

Splittings

FittingC2×C3×C5×C4⋊Q8 ⋊ C2
HallC3×C5 ⋊ C2×#486
SylowC3 ⋊ C2×C5×#486

Subgroups

subgroupG/H
centerC23×C5C2×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×C4⋊Q8C2
socleC23×C3×C5C2×D4
prime radicalC2×C5×#874C2
hypercenterC2×C5×C4⋊Q8D3
hypocenterC3C2×C5×#486
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C2×C5×C4⋊Q8

1056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 163342);