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C4×C5×C8×Dic3 #14294182

order1920
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C42×C5×C8 · Schur multiplier (H2) = C43

Aliases

direct productC4×C5×C8×Dic3

Splittings

derived, SylowC3 ⋊ C42×C5×C8
HallC3×C5 ⋊ C42×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5×C8D3
commutator, hypocenterC3C42×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
LCSG ▷ C3
UCSC1 ◁ C2×C4×C5×C8

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19880);