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#14412723

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

Aliases

No aliases for this group.

Splittings

FittingC3×C5×2−1+4 ⋊ C4
HallC3×C5 ⋊ #2898
SylowC5 ⋊ #84111
SylowC3 ⋊ #10617561

Subgroups

subgroupG/H
centerC2C22×#6763
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC3×C5×2−1+4C4
socleC2×C3×C5C22×C22⋊C4
prime radicalC3×D5×2−1+4C2
cosocleC3×C4×D5C24
hypercenter2−1+4ΓL(1,𝔽16)
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

1452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

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

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138421);