Finite Group Databasebeta

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C107×C22⋊(C7⋊C9) #41004076

order26964
automorphism?
homologyAbelianization (H1) = C9×C107 · Schur multiplier (H2) = C2

Aliases

direct productC107×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C7⋊C9×C107)
unambiguous semidirect productC7⋊(C22⋊C9×C107)
unambiguous semidirect product(C22×C107)⋊(C7⋊C9)
unambiguous semidirect product(C7×C107)⋊(C22⋊C9)

Splittings

derived, HallC22×C7 ⋊ C9×C107
HallC22×C7×C107 ⋊ C9
HallC7×C107 ⋊ C22⋊C9
HallC22×C107 ⋊ C7⋊C9
SylowC7 ⋊ C22⋊C9×C107
SylowC22 ⋊ C7⋊C9×C107

Subgroups

subgroupG/H
center, hypercenterC3×C107C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C9×C107
FrattiniC3C22⋊ΓL(1,𝔽8)×C107
Fitting, socle, prime radicalC22×C3×C7×C107C3
cosocleC22×C3×C7C3×C107
LCSG ▷ C22×C7
UCSC1 ◁ C3×C107

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13482

Conjugacy classes & character table

3852 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 25);