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#14312391

order1920
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

HallC3×C5 ⋊ #2101
SylowC5 ⋊ #68812
SylowC3 ⋊ #10599637

Subgroups

subgroupG/H
centerC23#6790
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socle, prime radicalC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2101
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Polycyclic presentation:

2^7,3,5|a^2=dg,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^2,i^a=i^4,c^b=cf,f^b=fg,i^b=i^4,f^c=fg

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38089);