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#14413411

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

FittingC2×C3×C5×M16 ⋊ C4
HallC3×C5 ⋊ #2911
SylowC5 ⋊ #83752
SylowC3 ⋊ #10617409

Subgroups

subgroupG/H
centerC4C2×C4⋊ΓL(1,𝔽16)
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC2×C3×C5×M16C4
socleC2×C3×C5C22×C4⋊C4
prime radicalC23×C3×D5D4
cosocleC3×C4×D5C24
hypercenterC2×M16ΓL(1,𝔽16)
hypocenterC3×C5#2911
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Polycyclic presentation:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 139109);