Finite Group Databasebeta

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C11×D1113 #37587499

order24486
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1113
unambiguous semidirect productC3⋊(C11×D371)
unambiguous semidirect productC7⋊(C11×D159)
unambiguous semidirect productC53⋊(C11×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C53 ⋊ C2
derived, HallC3×C7×C53 ⋊ C2×C11
HallC7×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ D7
HallC11×C53 ⋊ D21
HallC7×C53 ⋊ D3×C11
HallC3×C7×C11 ⋊ D53
HallC3×C53 ⋊ C11×D7
HallC7×C11 ⋊ D159
SylowC53 ⋊ C11×D21
HallC3×C11 ⋊ D371
HallC3×C7 ⋊ C11×D53
SylowC7 ⋊ C11×D159
SylowC3 ⋊ C11×D371

Subgroups

subgroupG/H
center, hypercenterC11D1113
commutator, cosocle, hypocenterC3×C7×C53C2×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C53C2
LCSG ▷ C3×C7×C53
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12243

Conjugacy classes & character table

6138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24486, 15);