Finite Group Databasebeta

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C2×C9×D113⋊C7 #43249771

order28476
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D113⋊C7
unambiguous semidirect productD113⋊(C2×C7×C9)
unambiguous semidirect product(C2×D113)⋊(C7×C9)
unambiguous semidirect product(C113⋊C7)⋊(C22×C9)
unambiguous semidirect product(C2×C113⋊C7)⋊(C2×C9)
unambiguous semidirect product(C2×C9×D113)⋊C7

Splittings

FittingC2×C9×C113 ⋊ C2×C7
derived, SylowC113 ⋊ C22×C7×C9
HallC9×C113⋊C7 ⋊ C22
HallC2×C9×D113 ⋊ C7
HallC9×C113 ⋊ C22×C7
HallC113⋊C7 ⋊ C22×C9
HallC2×D113 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9D113⋊C7
commutator, hypocenterC113C22×C7×C9
FrattiniC3C2×C3×D113⋊C7
FittingC2×C9×C113C2×C7
socleC2×C3×C113C2×C3×C7
prime radicalC2×C3×D113⋊C7C3
cosocleC3×C113C22×C3×C7
LCSG ▷ C113
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2034

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28476, 22);