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C3×C4×#4011 #14295372

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC3×C4×#4011

Splittings

FittingC23×C3×C4×C5 ⋊ C4
HallC3×C5 ⋊ C4×#99
SylowC5 ⋊ C3×C4×#99

Subgroups

subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C22
cosocleC23×D5C23×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C3×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C23×C3×C4

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21070);