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#13062489

order1350
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C5

Aliases

No aliases for this group.

Splittings

FittingC52×C9 ⋊ C2×C3
HallC9⋊(C52⋊C3) ⋊ C2
HallC5⋊D5 ⋊ 3−1+2
SylowC52 ⋊ C2×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C3×(C5⋊D5)⋊C3
commutator, socle, cosocleC3×C52C2×C32
FittingC52×C9C2×C3
prime radicalC3×(C5⋊D5)⋊C3C3
hypercenterC9(C5⋊D5)⋊C3
hypocenterC52C2×3−1+2
LCSG ▷ C3×C52 ▷ C52
UCSC1 ◁ C3 ◁ C9

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Polycyclic presentation:

2,3^3,5^2|c^3=d^2,e^a=e^4,f^a=f^4,c^b=cd,e^b=ef,f^b=e^2f^3

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1350, 48);