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C5×C11×Dic63 #28357347

order13860
isoclinismisoclinic class of D63
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic63
unambiguous semidirect productC7⋊(C5×C11×Dic9)
unambiguous semidirect productC9⋊(C5×C11×Dic7)

Splittings

derived, HallC7×C9 ⋊ C4×C5×C11
HallC5×C7×C9×C11 ⋊ C4
HallC7×C9×C11 ⋊ C4×C5
HallC5×C9×C11 ⋊ Dic7
HallC5×C7×C11 ⋊ Dic9
HallC5×C7×C9 ⋊ C4×C11
HallC9×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×Dic9
HallC5×C9 ⋊ C11×Dic7
HallC5×C7 ⋊ C11×Dic9
SylowC9 ⋊ C5×C11×Dic7
SylowC7 ⋊ C5×C11×Dic9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D63
commutator, hypocenterC7×C9C4×C5×C11
FrattiniC2×C3C5×C11×D21
FittingC2×C5×C7×C9×C11C2
socle, prime radicalC2×C3×C5×C7×C11D3
cosocleC2×C7×C9C2×C5×C11
LCSG ▷ C7×C9
UCSC1 ◁ C2×C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13860

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 14);