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#14296281

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

No aliases for this group.

Splittings

HallC3×C5 ⋊ C8×C4⋊C4
SylowC5 ⋊ #68651
SylowC3 ⋊ C4⋊C4×#170

Subgroups

subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C2×C4×C8
FittingC22×C3×C4×C5C2×C4
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C8×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Polycyclic presentation:

2^7,3,5|a^2=e,b^2=f,c^2=de,e^2=g,b^a=bd,i^a=i^2,h^c=h^2,i^c=i^2,i^e=i^4

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21979);