Finite Group Databasebeta

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C5×#63118⋊C9 #26043353

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

Aliases

direct productC5×#63118⋊C9
unambiguous semidirect product#63118⋊(C5×C9)
unambiguous semidirect product(C5×#63118)⋊C9

Splittings

derivedC5×C13 ⋊ C4×C5×C9
HallC52×C13⋊C9 ⋊ C4
HallC5×#63118 ⋊ C9
HallC52×C13 ⋊ C4×C9
HallC13⋊C9 ⋊ C5×Dic5
SylowC52 ⋊ #261⋊C9
SylowC13 ⋊ C5×C9×Dic5

Subgroups

subgroupG/H
center, hypercenterC3×C5#63118⋊C3
commutator, hypocenterC5×C13C4×C5×C9
FrattiniC3C5×#63118⋊C3
Fitting, socleC3×C52×C13C3×C4
prime radicalC3×C52×D13C2×C3
cosocleC3×C5×D13C2×C3×C5
LCSG ▷ C5×C13
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

435 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 200);