Finite Group Databasebeta

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C2×D15×#100 #14412040

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D15×#100

Splittings

FittingC2×C3×C5×#100 ⋊ C2
HallC3×C5 ⋊ C22×#100
SylowC5 ⋊ C2×D3×#100
SylowC3 ⋊ C2×D5×#100

Subgroups

subgroupG/H
centerC22C22⋊C4×D15
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#100C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D4×D15C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#100D15
hypocenterC3×C5C22×#100
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

1984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137738);