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#14412951

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

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×Q8 ⋊ C2×C4
HallC3×C5 ⋊ #2901
SylowC5 ⋊ #78983
SylowC3 ⋊ #10617562

Subgroups

subgroupG/H
centerC2C2×D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC2×C3×C5C22×C22⋊C4
prime radical#11757048C2
cosocleC3×C4×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2901
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

1476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

2^7,3,5|a^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,i^a=i^2,e^b=eg,i^b=i^4,d^c=dg,h^d=h^2,i^f=i^4

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138649);