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C4×(C151⋊C5)⋊C9 #41029987

order27180
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×(C151⋊C5)⋊C9
unambiguous semidirect product(C4×C151⋊C5)⋊C9
unambiguous semidirect product(C4×C151⋊C9)⋊C5

Splittings

derived, SylowC151 ⋊ C4×C5×C9
HallC4×C151⋊C9 ⋊ C5
HallC4×C151⋊C5 ⋊ C9
HallC151⋊C9 ⋊ C4×C5
HallC151⋊C5 ⋊ C4×C9
HallC4×C151 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4(C151⋊C3)⋊C5
commutator, hypocenterC151C4×C5×C9
FrattiniC2×C3C2×(C151⋊C3)⋊C5
FittingC3×C4×C151C3×C5
socle, cosocleC2×C3×C151C2×C3×C5
prime radicalC2×C3×C151⋊C5C2×C3
LCSG ▷ C151
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5436

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27180, 4);