Finite Group Databasebeta

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C2×C11⋊((C7⋊C9)⋊D13) #49114440

order36036
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊((C7⋊C9)⋊D13)
unambiguous semidirect product(C2×C11)⋊((C7⋊C9)⋊D13)
unambiguous semidirect product(C2×C7⋊C9)⋊D143

Splittings

derived, HallC7×C11×C13 ⋊ C22×C9
HallC11×C13×C7⋊C9 ⋊ C22
HallC2×D1001 ⋊ C9
HallC13×C7⋊C9 ⋊ C2×D11
HallC11×C7⋊C9 ⋊ C2×D13
HallC11×C13 ⋊ C2×D7⋊C9
HallC7×C13 ⋊ C2×C9×D11
HallC7×C11 ⋊ C2×C9×D13
HallC7⋊C9 ⋊ C2×D143
SylowC13 ⋊ C2×C11⋊(D7⋊C9)
SylowC11 ⋊ C2×(C7⋊C9)⋊D13
SylowC7 ⋊ C2×C9×D143

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊(ΓL(1,𝔽8)⋊D13)
commutator, hypocenterC7×C11×C13C22×C9
FrattiniC3C2×C11⋊(ΓL(1,𝔽8)⋊D13)
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×D1001C3
cosocleC3×C7×C11×C13C22×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

2172 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 108);