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D4×#6712 #14326997

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#6712

Splittings

HallC3×C5 ⋊ D4×C4⋊C4
SylowC5 ⋊ D4×Dic3⋊C4
SylowC3 ⋊ D4×#683

Subgroups

subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C4×C5×D4C2
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×C4×D4D15
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

1552 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, 52695);