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#14296192

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

Aliases

No aliases for this group.

Splittings

FittingC3×C5×C4⋊C8 ⋊ C4
HallC3×C5 ⋊ #1768
SylowC5 ⋊ #70442
SylowC3 ⋊ #10604029

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C2×C42
FittingC3×C5×C4⋊C8C4
prime radicalC22×C3×D5C22×C4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C8ΓL(1,𝔽16)
hypocenterC3×C5#1768
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4⋊C8

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,c^a=cg,h^a=h^2,i^a=i^3,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, 21890);