Finite Group Databasebeta

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D11×D741 #45656804

order32604
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD11×D741
unambiguous semidirect product(C3×D11)⋊D247
unambiguous semidirect product(C13×D11)⋊D57
unambiguous semidirect product(C19×D11)⋊D39

Splittings

Fitting, socle, derived, HallC3×C11×C13×C19 ⋊ C22
HallC11×C13×C19 ⋊ C2×D3
HallC3×C13×C19 ⋊ C2×D11
HallC3×C11×C19 ⋊ C2×D13
HallC3×C11×C13 ⋊ C2×D19
HallC13×C19 ⋊ D3×D11
HallC11×C19 ⋊ C2×D39
HallC11×C13 ⋊ C2×D57
HallC3×C19 ⋊ D11×D13
HallC3×C13 ⋊ D11×D19
HallC3×C11 ⋊ C2×D247
SylowC19 ⋊ D11×D39
SylowC13 ⋊ D11×D57
SylowC11 ⋊ C2×D741
SylowC3 ⋊ D11×D247

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C13×C19C22
LCSG ▷ C3×C11×C13×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8151

Conjugacy classes & character table

2604 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 154);