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C22×C3×C8×Dic5 #14411161

order1920
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C3×C8×Dic5

Splittings

derived, SylowC5 ⋊ C22×C3×C4×C8
HallC3×C5 ⋊ C22×C4×C8

Subgroups

subgroupG/H
center, hypercenterC23×C3×C8D5
commutator, hypocenterC5C22×C3×C4×C8
FrattiniC2×C4C23×C3×D5
FittingC23×C3×C5×C8C2
socle, prime radicalC24×C3×C5C2×C4
cosocleC2×C4×C5C24×C3
LCSG ▷ C5
UCSC1 ◁ C23×C3×C8

1520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136859);