Finite Group Databasebeta

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C7×D2223 #44527542

order31122
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2223
unambiguous semidirect productC9⋊(C7×D247)
unambiguous semidirect productC13⋊(C7×D171)
unambiguous semidirect productC19⋊(C7×D117)

Splittings

Fitting, HallC7×C9×C13×C19 ⋊ C2
derived, HallC9×C13×C19 ⋊ C2×C7
HallC7×C13×C19 ⋊ D9
HallC7×C9×C19 ⋊ D13
HallC7×C9×C13 ⋊ D19
HallC13×C19 ⋊ C7×D9
HallC9×C19 ⋊ C7×D13
HallC7×C19 ⋊ D117
HallC9×C13 ⋊ C7×D19
HallC7×C13 ⋊ D171
HallC7×C9 ⋊ D247
SylowC19 ⋊ C7×D117
SylowC13 ⋊ C7×D171
SylowC9 ⋊ C7×D247

Subgroups

subgroupG/H
center, hypercenterC7D2223
commutator, cosocle, hypocenterC9×C13×C19C2×C7
FrattiniC3C7×D741
FittingC7×C9×C13×C19C2
socleC3×C7×C13×C19D3
LCSG ▷ C9×C13×C19
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15561

Conjugacy classes & character table

7791 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 25);