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C7×D2091 #44418079

order29274
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2091
unambiguous semidirect productC3⋊(C7×D697)
unambiguous semidirect productC17⋊(C7×D123)
unambiguous semidirect productC41⋊(C7×D51)

Splittings

Fitting, socle, HallC3×C7×C17×C41 ⋊ C2
derived, HallC3×C17×C41 ⋊ C2×C7
HallC7×C17×C41 ⋊ D3
HallC3×C7×C41 ⋊ D17
HallC17×C41 ⋊ D3×C7
HallC3×C7×C17 ⋊ D41
HallC7×C41 ⋊ D51
HallC3×C41 ⋊ C7×D17
HallC7×C17 ⋊ D123
HallC3×C17 ⋊ C7×D41
SylowC41 ⋊ C7×D51
HallC3×C7 ⋊ D697
SylowC17 ⋊ C7×D123
SylowC3 ⋊ C7×D697

Subgroups

subgroupG/H
center, hypercenterC7D2091
commutator, cosocle, hypocenterC3×C17×C41C2×C7
FrattiniC1G
Fitting, socleC3×C7×C17×C41C2
LCSG ▷ C3×C17×C41
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14637

Conjugacy classes & character table

7329 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29274, 13);