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#14279964

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×C4⋊C4 ⋊ C4
HallC3×C5 ⋊ #1436
SylowC5 ⋊ #71564
SylowC3 ⋊ #10604343

Subgroups

subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C2×C42
FittingC2×C3×C5×C4⋊C4C4
socleC23×C3×C5C22×C4
prime radical, cosocleC23×C3×D5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1436
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

1224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=f,b^2=g,c^2=f,b^a=bd,c^a=ce,h^b=h^2,i^b=i^2,i^g=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, 5662);