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#14277176

order1920
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

HallC3×C5 ⋊ #1296
SylowC5 ⋊ #67634
SylowC3 ⋊ #10598725

Subgroups

subgroupG/H
centerC23#6763
commutatorC2×C3×C4×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socle, prime radicalC23×C3×C5C22⋊C4
cosocleC2×C3×C4×Dic5C22
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1296
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Polycyclic presentation:

2^7,3,5|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,c^b=cg,h^b=h^2,i^b=i^2,i^e=i^4

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2874);