Finite Group Databasebeta

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C11×C13×Dic7⋊C9 #49114366

order36036
automorphism?
homologyAbelianization (H1) = C4×C9×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×Dic7⋊C9
unambiguous semidirect productDic7⋊(C9×C11×C13)
unambiguous semidirect product(C7⋊C9)⋊(C4×C11×C13)
unambiguous semidirect product(C11×Dic7)⋊(C9×C13)

Splittings

derived, SylowC7 ⋊ C4×C9×C11×C13
HallC11×C13×C7⋊C9 ⋊ C4
HallC11×C13×Dic7 ⋊ C9
HallC7×C11×C13 ⋊ C4×C9
HallC13×C7⋊C9 ⋊ C4×C11
HallC11×C7⋊C9 ⋊ C4×C13
HallC13×Dic7 ⋊ C9×C11
HallC11×Dic7 ⋊ C9×C13
HallC7×C13 ⋊ C4×C9×C11
HallC7×C11 ⋊ C4×C9×C13
HallC7⋊C9 ⋊ C4×C11×C13
HallDic7 ⋊ C9×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13AGL(1,𝔽7)
commutator, hypocenterC7C4×C9×C11×C13
FrattiniC2×C3C11×C13×AGL(1,𝔽7)
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2×C3
cosocleC2×C3×C7C2×C3×C11×C13
LCSG ▷ C7
UCSC1 ◁ C2×C3×C11×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 34);