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#14429392

order1920
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingC3×C5×AGL(1,ℤ/8) ⋊ C22
HallC3×C5 ⋊ C2×#472
SylowC5 ⋊ D3×#472
SylowC3 ⋊ D5×#472

Subgroups

subgroupG/H
centerC2#11755049
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×AGL(1,ℤ/8)C22
socleC2×C3×C5C2×#121
hypercenterAGL(1,ℤ/8)D3×D5
hypocenterC3×C5C2×#472
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^7,3,5|b^2=eg,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^2,f^c=fg,h^d=h^2,i^d=i^4

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 155090);