Finite Group Databasebeta

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C7×C13×D61⋊C3 #45686563

order33306
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×D61⋊C3
unambiguous semidirect productD61⋊(C3×C7×C13)
unambiguous semidirect product(C61⋊C3)⋊(C2×C7×C13)

Splittings

Fitting, socle, HallC7×C13×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C2×C3×C7×C13
HallC7×C13×C61⋊C3 ⋊ C2
HallC7×C13×D61 ⋊ C3
HallC13×C61⋊C3 ⋊ C2×C7
HallC13×D61 ⋊ C3×C7
HallC7×C61⋊C3 ⋊ C2×C13
HallC7×D61 ⋊ C3×C13
HallC13×C61 ⋊ C2×C3×C7
HallC7×C61 ⋊ C2×C3×C13
HallC61⋊C3 ⋊ C2×C7×C13
HallD61 ⋊ C3×C7×C13

Subgroups

subgroupG/H
center, hypercenterC7×C13D61⋊C3
commutator, cosocle, hypocenterC61C2×C3×C7×C13
FrattiniC1G
Fitting, socleC7×C13×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C7×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5551

Conjugacy classes & character table

1456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33306, 30);