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C11×(C7⋊C9)⋊Dic5 #28357365

order13860
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C7⋊C9)⋊Dic5
unambiguous semidirect product(C7⋊C9)⋊(C11×Dic5)
unambiguous semidirect productDic35⋊(C9×C11)
unambiguous semidirect product(C11×Dic35)⋊C9

Splittings

derived, HallC5×C7 ⋊ C4×C9×C11
HallC5×C11×C7⋊C9 ⋊ C4
HallC11×Dic35 ⋊ C9
HallC11×C7⋊C9 ⋊ Dic5
HallC5×C7×C11 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C11
HallDic35 ⋊ C9×C11
HallC7×C11 ⋊ C9×Dic5
HallC7⋊C9 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic7⋊C9
SylowC7 ⋊ C9×C11×Dic5
SylowC5 ⋊ C11×Dic7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C4×C9×C11
FrattiniC2×C3C11×C5⋊AGL(1,𝔽7)
Fitting, socle, prime radicalC2×C3×C5×C7×C11C2×C3
cosocleC2×C3×C5×C7C2×C3×C11
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13860

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 32);