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C2×C4×C5×#217 #14319376

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×C5×#217

Splittings

HallC3×C5 ⋊ C2×C4×C22⋊C4
SylowC3 ⋊ C2×C4×C5×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4×C5C2×D3
commutatorC2×C3C22×C42×C5
FrattiniC23C23×C5×D3
FittingC24×C3×C4×C5C2
socleC24×C3×C5C23
prime radicalC25×C3×C5C22
cosocleC23×C3C24×C5
hypercenterC24×C4×C5D3
hypocenterC3C2×C4×C5×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C4×C5 ◁ C24×C4×C5

2720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45074);