Finite Group Databasebeta

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C2×C7⋊C9×D55 #28357409

order13860
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7⋊C9×D55
unambiguous semidirect product(C2×C5)⋊(D11×C7⋊C9)
unambiguous semidirect product(C2×C11)⋊(D5×C7⋊C9)
unambiguous semidirect product(C2×C7×D55)⋊C9

Splittings

derived, HallC5×C7×C11 ⋊ C22×C9
HallC5×C11×C7⋊C9 ⋊ C22
HallC2×C7×D55 ⋊ C9
HallC11×C7⋊C9 ⋊ C2×D5
HallC5×C7⋊C9 ⋊ C2×D11
HallC7×C11 ⋊ C2×C9×D5
HallC5×C11 ⋊ C22×C7⋊C9
HallC5×C7 ⋊ C2×C9×D11
SylowC11 ⋊ C2×D5×C7⋊C9
SylowC7 ⋊ C2×C9×D55
SylowC5 ⋊ C2×D11×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D55
commutator, hypocenterC5×C7×C11C22×C9
FrattiniC3C2×ΓL(1,𝔽8)×D55
Fitting, socleC2×C3×C5×C7×C11C2×C3
prime radicalC2×C3×C7×D55C3
cosocleC3×C5×C7×C11C22×C3
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6930

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 76);