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C3×#10602422 #14300151

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×#10602422

Splittings

HallC3×C5 ⋊ #1865
SylowC5 ⋊ C3×#1865

Subgroups

subgroupG/H
centerC23×C3C2×C22⋊D5
commutatorC2×C4×C5C22×C3×C4
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×Q8C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C4×C5C23×C3
hypercenterC2×C3×C4×Q8D5
hypocenterC5C3×#1865
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

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, 25849);