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C9×C11×C7⋊Dic7 #34084647

order19404
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C7

Aliases

direct productC9×C11×C7⋊Dic7

Splittings

derived, SylowC72 ⋊ C4×C9×C11
HallC72×C9×C11 ⋊ C4
HallC72×C11 ⋊ C4×C9
HallC72×C9 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11C7⋊D7
commutator, hypocenterC72C4×C9×C11
FrattiniC2×C3C3×C11×C7⋊D7
FittingC2×C72×C9×C11C2
socle, prime radicalC2×C3×C72×C11C2×C3
cosocleC2×C3×C72C2×C3×C11
LCSG ▷ C72
UCSC1 ◁ C2×C9×C11

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19404

Conjugacy classes & character table

5148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 138);