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C2×#11751287 #14423348

order1920
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#11751287

Splittings

FittingC22×C3×C5×Q16 ⋊ C2
HallC3×C5 ⋊ C2×#451
SylowC5 ⋊ C2×#5186
SylowC3 ⋊ C2×#65475

Subgroups

subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×Q16C2
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
hypercenterC22×Q16D15
hypocenterC3×C5C2×#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

1480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 149046);