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C5×Dic3×SD32 #14315355

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×Dic3×SD32

Splittings

HallC3×C5 ⋊ C4×SD32
SylowC3 ⋊ C4×C5×SD32

Subgroups

subgroupG/H
centerC22×C5D3×D8
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C5×SD32C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×C5×D8C22
cosocleC2×C3×C8C23×C5
hypercenterC2×C5×SD32D3
hypocenterC3C4×C5×SD32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C2×C5×SD32

324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 41053);