Finite Group Databasebeta

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C2×C7×D61⋊C9 #29506728

order15372
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D61⋊C9
unambiguous semidirect productD61⋊(C2×C7×C9)
unambiguous semidirect product(C2×D61)⋊(C7×C9)
unambiguous semidirect product(C61⋊C9)⋊(C22×C7)
unambiguous semidirect product(C2×C61⋊C9)⋊(C2×C7)

Splittings

derived, SylowC61 ⋊ C22×C7×C9
HallC7×C61⋊C9 ⋊ C22
HallC2×C7×D61 ⋊ C9
HallC61⋊C9 ⋊ C22×C7
HallC7×C61 ⋊ C22×C9
HallC2×D61 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D61⋊C3
commutator, hypocenterC61C22×C7×C9
FrattiniC3C2×C7×D61⋊C3
Fitting, socleC2×C3×C7×C61C2×C3
prime radicalC2×C3×C7×D61C3
cosocleC3×C61C22×C3×C7
LCSG ▷ C61
UCSC1 ◁ C2×C3×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7686

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 38);