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C72×C11×Dic9 #34084649

order19404
automorphism?
homologyAbelianization (H1) = C4×C72×C11 · Schur multiplier (H2) = C7

Aliases

direct productC72×C11×Dic9
unambiguous semidirect productC9⋊(C4×C72×C11)

Splittings

derived, SylowC9 ⋊ C4×C72×C11
HallC72×C9×C11 ⋊ C4
HallC72×C9 ⋊ C4×C11
HallC9×C11 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72×C11D9
commutator, hypocenterC9C4×C72×C11
FrattiniC2×C3D3×C72×C11
FittingC2×C72×C9×C11C2
socle, prime radicalC2×C3×C72×C11D3
cosocleC2×C9C2×C72×C11
LCSG ▷ C9
UCSC1 ◁ C2×C72×C11

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19404

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 140);