Finite Group Databasebeta

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C7×(C7⋊C9)⋊#261 #37524405

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

Aliases

direct productC7×(C7⋊C9)⋊#261
unambiguous semidirect product(C7⋊C9)⋊(C7×#261)

Splittings

derivedC7×C13 ⋊ C4×C7×C9
HallC7×C13×C7⋊C9 ⋊ C4
HallC7×C7⋊#261 ⋊ C9
HallC72×C13 ⋊ C4×C9
HallC7×C7⋊C9 ⋊ #261
SylowC72 ⋊ C9×#261
SylowC13 ⋊ C7×Dic7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C7ΓL(1,𝔽8)⋊#261
commutator, hypocenterC7×C13C4×C7×C9
FrattiniC3C7×ΓL(1,𝔽8)⋊#261
Fitting, socleC3×C72×C13C3×C4
prime radicalC3×C72×D13C2×C3
cosocleC3×C7×D13C2×C3×C7
LCSG ▷ C7×C13
UCSC1 ◁ C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1638

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 350);