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#14326162

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

No aliases for this group.

Splittings

HallC3×C5 ⋊ Q8×C22⋊C4
SylowC5 ⋊ #76614
SylowC3 ⋊ Q8×C22⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×Q8C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5Q8×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Polycyclic presentation:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51860);