Finite Group Databasebeta

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C4×C7×C11×C7⋊C9 #34084641

order19404
automorphism?
homologyAbelianization (H1) = C4×C7×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C11×C7⋊C9
unambiguous semidirect product(C4×C7)⋊(C7×C9×C11)
unambiguous semidirect product(C4×C7×C11)⋊(C7×C9)

Splittings

derivedC7 ⋊ C4×C7×C9×C11
HallC4×C72×C11 ⋊ C9
HallC72×C11 ⋊ C4×C9
HallC4×C72 ⋊ C9×C11
SylowC72 ⋊ C4×C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7×C11ΓL(1,𝔽8)
commutator, hypocenterC7C4×C7×C9×C11
FrattiniC2×C3C2×C7×C11×ΓL(1,𝔽8)
FittingC3×C4×C72×C11C3
socle, prime radicalC2×C3×C72×C11C2×C3
cosocleC2×C3×C7C2×C3×C7×C11
LCSG ▷ C7
UCSC1 ◁ C3×C4×C7×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 132);