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C72×C9×Dic11 #34084644

order19404
automorphism?
homologyAbelianization (H1) = C4×C72×C9 · Schur multiplier (H2) = C7

Aliases

direct productC72×C9×Dic11
unambiguous semidirect productC11⋊(C4×C72×C9)

Splittings

derived, SylowC11 ⋊ C4×C72×C9
HallC72×C9×C11 ⋊ C4
HallC72×C11 ⋊ C4×C9
HallC9×C11 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72×C9D11
commutator, hypocenterC11C4×C72×C9
FrattiniC2×C3C3×C72×D11
FittingC2×C72×C9×C11C2
socle, prime radicalC2×C3×C72×C11C2×C3
cosocleC2×C3×C11C2×C3×C72
LCSG ▷ C11
UCSC1 ◁ C2×C72×C9

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19404

Conjugacy classes & character table

6174 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 135);