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C11×D861 #34038823

order18942
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D861
unambiguous semidirect productC3⋊(C11×D287)
unambiguous semidirect productC7⋊(C11×D123)
unambiguous semidirect productC41⋊(C11×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C41 ⋊ C2
derived, HallC3×C7×C41 ⋊ C2×C11
HallC7×C11×C41 ⋊ D3
HallC3×C11×C41 ⋊ D7
HallC11×C41 ⋊ D21
HallC7×C41 ⋊ D3×C11
HallC3×C7×C11 ⋊ D41
HallC3×C41 ⋊ C11×D7
HallC7×C11 ⋊ D123
SylowC41 ⋊ C11×D21
HallC3×C11 ⋊ D287
HallC3×C7 ⋊ C11×D41
SylowC7 ⋊ C11×D123
SylowC3 ⋊ C11×D287

Subgroups

subgroupG/H
center, hypercenterC11D861
commutator, cosocle, hypocenterC3×C7×C41C2×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C41C2
LCSG ▷ C3×C7×C41
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9471

Conjugacy classes & character table

4752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D21×D41, D11×D861, D451⋊D21, …
maximal normal subgroup ofC11×D21×D41, D11×D861, D451⋊D21, …
maximal quotient ofC11×Dic861, C2×C11×D861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18942, 15);