Finite Group Databasebeta

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C2×C11×D561 #37590667

order24684
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D561
unambiguous semidirect product(C2×C3)⋊(C11×D187)
unambiguous semidirect product(C2×C11)⋊(C11×D51)
unambiguous semidirect product(C2×C17)⋊(C11×D33)

Splittings

Fitting, socleC2×C3×C112×C17 ⋊ C2
derivedC3×C11×C17 ⋊ C22×C11
HallC3×C112×C17 ⋊ C22
HallC112×C17 ⋊ C2×D3
HallC3×C112 ⋊ C2×D17
SylowC112 ⋊ C2×D51
HallC3×C17 ⋊ C2×C11×D11
SylowC17 ⋊ C2×C11×D33
SylowC3 ⋊ C2×C11×D187

Subgroups

subgroupG/H
center, hypercenterC2×C11D561
commutator, cosocle, hypocenterC3×C11×C17C22×C11
FrattiniC1G
Fitting, socleC2×C3×C112×C17C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2244

Conjugacy classes & character table

6204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 113);