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C2×C5×Dic3×C16 #14312506

order1920
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C5×Dic3×C16

Splittings

derived, SylowC3 ⋊ C2×C4×C5×C16
HallC3×C5 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC22×C5×C16D3
commutator, hypocenterC3C2×C4×C5×C16
FrattiniC2×C8C22×C5×D3
FittingC22×C3×C5×C16C2
socle, prime radicalC23×C3×C5C2×C8
cosocleC2×C3×C8C23×C5
LCSG ▷ C3
UCSC1 ◁ C22×C5×C16

432 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, 38204);