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C2×D5×#824 #14412080

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

Aliases

direct productC2×D5×#824

Splittings

HallC3×C5 ⋊ C22×#101
SylowC5 ⋊ C22×#824
SylowC3 ⋊ C2×D5×#101

Subgroups

subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5C22×#101
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

1472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137778);