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C4×#91174 #14295448

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#91174

Splittings

HallC3×C5 ⋊ C4×#100
SylowC5 ⋊ C4×#823
SylowC3 ⋊ C4×#4013

Subgroups

subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1203C22
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#100
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21146);