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C9×AGL(1,𝔽5)×C149 #41001225

order26820
automorphism?
homologyAbelianization (H1) = C4×C9×C149 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽5)×C149

Splittings

Fitting, HallC5×C9×C149 ⋊ C4
derived, SylowC5 ⋊ C4×C9×C149
HallC5×C149 ⋊ C4×C9
HallC5×C9 ⋊ C4×C149

Subgroups

subgroupG/H
center, hypercenterC9×C149AGL(1,𝔽5)
commutator, hypocenterC5C4×C9×C149
FrattiniC3C3×AGL(1,𝔽5)×C149
FittingC5×C9×C149C4
socleC3×C5×C149C3×C4
prime radicalC3×D5×C149C2×C3
cosocleC3×D5C2×C3×C149
LCSG ▷ C5
UCSC1 ◁ C9×C149

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6705

Conjugacy classes & character table

6705 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 11);