Finite Group Databasebeta

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C7×C9×C7⋊#261 #37524560

order22932
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C7⋊#261

Splittings

Fitting, HallC72×C9×C13 ⋊ C4
derivedC7×C13 ⋊ C4×C7×C9
HallC72×C13 ⋊ C4×C9
HallC72×C9 ⋊ #261
HallC9×C13 ⋊ C7×Dic7
SylowC72 ⋊ C9×#261
SylowC13 ⋊ C7×C9×Dic7

Subgroups

subgroupG/H
center, hypercenterC7×C9C7⋊#261
commutator, hypocenterC7×C13C4×C7×C9
FrattiniC3C3×C7×C7⋊#261
FittingC72×C9×C13C4
socleC3×C72×C13C3×C4
prime radicalC3×C72×D13C2×C3
cosocleC3×C7×D13C2×C3×C7
LCSG ▷ C7×C13
UCSC1 ◁ C7×C9

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1638

Conjugacy classes & character table

1953 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 505);