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C9×C11×#63118 #38787872

order25740
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×#63118

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C4
derived, HallC5×C13 ⋊ C4×C9×C11
HallC9×C11×C13 ⋊ Dic5
HallC5×C11×C13 ⋊ C4×C9
HallC5×C9×C13 ⋊ C4×C11
HallC5×C9×C11 ⋊ #261
HallC11×C13 ⋊ C9×Dic5
HallC9×C13 ⋊ C11×Dic5
HallC5×C11 ⋊ C9×#261
HallC5×C9 ⋊ C11×#261
SylowC13 ⋊ C9×C11×Dic5
SylowC5 ⋊ C9×C11×#261

Subgroups

subgroupG/H
center, hypercenterC9×C11#63118
commutator, hypocenterC5×C13C4×C9×C11
FrattiniC3C3×C11×#63118
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13C3×C4
prime radicalC3×C5×C11×D13C2×C3
cosocleC3×C5×D13C2×C3×C11
LCSG ▷ C5×C13
UCSC1 ◁ C9×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2277 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 103);