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#14330622

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

FittingC3×C5×C22⋊C4 ⋊ C2×C4
HallC3×C5 ⋊ #2374
SylowC5 ⋊ #75488
SylowC3 ⋊ #10617307

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2374
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^7,3,5|a^2=g,b^2=g,c^2=ef,d^2=ef,b^a=be,c^a=cf,i^a=i^3,d^b=de,i^b=i^2,h^c=h^2,h^d=h^2,i^g=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, 56320);