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C11⋊C5×Dic63 #28357358

order13860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic63
unambiguous semidirect productC7⋊(Dic9×C11⋊C5)
unambiguous semidirect productC9⋊(Dic7×C11⋊C5)
unambiguous semidirect product(C11×Dic63)⋊C5

Splittings

derived, HallC7×C9×C11 ⋊ C4×C5
HallC7×C9×C11⋊C5 ⋊ C4
HallC11×Dic63 ⋊ C5
HallC9×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ Dic9
HallC9×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×Dic9
HallC7×C9 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×Dic63
SylowC9 ⋊ Dic7×C11⋊C5
SylowC7 ⋊ Dic9×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D63
commutator, hypocenterC7×C9×C11C4×C5
FrattiniC2×C3D21×C11⋊C5
Fitting, cosocleC2×C7×C9×C11C2×C5
socleC2×C3×C7×C11C5×D3
prime radicalC2×C3×C7×C11⋊C5D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 25);