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C11×C7⋊Dic63 #34084653

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

Aliases

direct productC11×C7⋊Dic63
unambiguous semidirect productC7⋊(C11×Dic63)
unambiguous semidirect productC9⋊(C11×C7⋊Dic7)

Splittings

derived, HallC72×C9 ⋊ C4×C11
HallC72×C9×C11 ⋊ C4
HallC72×C11 ⋊ Dic9
HallC9×C11 ⋊ C7⋊Dic7
SylowC72 ⋊ C11×Dic9
SylowC9 ⋊ C11×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C11C7⋊D63
commutator, hypocenterC72×C9C4×C11
FrattiniC2×C3C11×C3⋊(C7⋊D7)
FittingC2×C72×C9×C11C2
socle, prime radicalC2×C3×C72×C11D3
cosocleC2×C72×C9C2×C11
LCSG ▷ C72×C9
UCSC1 ◁ C2×C11

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19404

Conjugacy classes & character table

4884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 144);