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C9×C11⋊#63118 #38787874

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

Aliases

direct productC9×C11⋊#63118
unambiguous semidirect productC11⋊(C9×#63118)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C4
derived, HallC5×C11×C13 ⋊ C4×C9
HallC9×C11×C13 ⋊ Dic5
HallC5×C9×C13 ⋊ Dic11
HallC5×C9×C11 ⋊ #261
HallC11×C13 ⋊ C9×Dic5
HallC9×C13 ⋊ Dic55
HallC9×C11 ⋊ #63118
HallC5×C13 ⋊ C9×Dic11
HallC5×C11 ⋊ C9×#261
HallC5×C9 ⋊ C11⋊#261
SylowC13 ⋊ C9×Dic55
SylowC11 ⋊ C9×#63118
SylowC5 ⋊ C9×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC9C11⋊#63118
commutator, hypocenterC5×C11×C13C4×C9
FrattiniC3C3×C11⋊#63118
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13C3×C4
prime radical, cosocleC3×C5×C11×D13C2×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2007 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 105);