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#14323262

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

Aliases

No aliases for this group.

Splittings

FittingC3×C4×C5×Q8 ⋊ C4
HallC3×C5 ⋊ #2320
SylowC5 ⋊ #82454
SylowC3 ⋊ #10617210

Subgroups

subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC3×C4×C5×Q8C4
prime radical, cosocleC22×C3×D5C24
hypercenterC4×Q8ΓL(1,𝔽16)
hypocenterC3×C5#2320
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 48960);