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C5×#63122⋊C9 #26043349

order11700
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#63122⋊C9
unambiguous semidirect product#63122⋊(C5×C9)
unambiguous semidirect product(C5×#63122)⋊C9

Splittings

derivedC5×C13 ⋊ C4×C5×C9
HallC52×C13⋊C9 ⋊ C4
HallC5×#63122 ⋊ C9
HallC52×C13 ⋊ C4×C9
HallC13⋊C9 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ #261⋊C9
SylowC13 ⋊ C5×C9×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC3×C5#63122⋊C3
commutator, hypocenterC5×C13C4×C5×C9
FrattiniC3C5×#63122⋊C3
Fitting, socleC3×C52×C13C3×C4
prime radicalC3×C5×D65C2×C3
cosocleC3×D65C2×C3×C5
LCSG ▷ C5×C13
UCSC1 ◁ C3×C5

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

300 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 196);