Finite Group Databasebeta

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D11×D651 #43270703

order28644
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD11×D651
unambiguous semidirect product(C3×D11)⋊D217
unambiguous semidirect product(C7×D11)⋊D93
unambiguous semidirect product(D11×C31)⋊D21

Splittings

Fitting, socle, derived, HallC3×C7×C11×C31 ⋊ C22
HallC7×C11×C31 ⋊ C2×D3
HallC3×C11×C31 ⋊ C2×D7
HallC3×C7×C31 ⋊ C2×D11
HallC11×C31 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×D31
HallC7×C31 ⋊ D3×D11
HallC3×C31 ⋊ D7×D11
HallC7×C11 ⋊ C2×D93
HallC3×C11 ⋊ C2×D217
SylowC31 ⋊ D11×D21
HallC3×C7 ⋊ D11×D31
SylowC11 ⋊ C2×D651
SylowC7 ⋊ D11×D93
SylowC3 ⋊ D11×D217

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C31C22
LCSG ▷ C3×C7×C11×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7161

Conjugacy classes & character table

2289 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28644, 122);