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C11×C9⋊#63118 #38787896

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

Aliases

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

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C4
derived, HallC5×C9×C13 ⋊ C4×C11
HallC9×C11×C13 ⋊ Dic5
HallC5×C11×C13 ⋊ Dic9
HallC5×C9×C11 ⋊ #261
HallC11×C13 ⋊ Dic45
HallC9×C13 ⋊ C11×Dic5
HallC9×C11 ⋊ #63118
HallC5×C13 ⋊ C11×Dic9
HallC5×C11 ⋊ C9⋊#261
HallC5×C9 ⋊ C11×#261
SylowC13 ⋊ C11×Dic45
SylowC9 ⋊ C11×#63118
SylowC5 ⋊ C11×C9⋊#261

Subgroups

subgroupG/H
center, hypercenterC11C9⋊#63118
commutator, hypocenterC5×C9×C13C4×C11
FrattiniC3C11×C3⋊#63118
FittingC5×C9×C11×C13C4
socleC3×C5×C11×C13Dic3
prime radicalC3×C5×C11×D13D3
cosocleC5×C9×D13C2×C11
LCSG ▷ C5×C9×C13
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2013 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 127);