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C3×#10602348 #14299353

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×#10602348

Splittings

HallC3×C5 ⋊ #1852
SylowC5 ⋊ C3×#1852

Subgroups

subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C4×C5C23×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C3×#1852
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25051);