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C4×#91766 #14319482

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#91766

Splittings

HallC3×C5 ⋊ C4×#117
SylowC5 ⋊ C4×#877
SylowC3 ⋊ C4×#4023

Subgroups

subgroupG/H
centerC22×C4C22×D15
commutatorC2×C3×C5C22×C42
FrattiniC23C23×D15
FittingC3×C4×C5×C22⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC4×C22⋊C4D15
hypocenterC3×C5C4×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

1504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45180);