Finite Group Databasebeta

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C7×C9×Dic77 #34084646

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

Aliases

direct productC7×C9×Dic77
unambiguous semidirect productC11⋊(C7×C9×Dic7)

Splittings

derivedC7×C11 ⋊ C4×C7×C9
HallC72×C9×C11 ⋊ C4
HallC72×C11 ⋊ C4×C9
HallC72×C9 ⋊ Dic11
HallC9×C11 ⋊ C7×Dic7
SylowC72 ⋊ C9×Dic11
SylowC11 ⋊ C7×C9×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D77
commutator, hypocenterC7×C11C4×C7×C9
FrattiniC2×C3C3×C7×D77
FittingC2×C72×C9×C11C2
socle, prime radicalC2×C3×C72×C11C2×C3
cosocleC2×C3×C7×C11C2×C3×C7
LCSG ▷ C7×C11
UCSC1 ◁ C2×C7×C9

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

5040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 137);