Finite Group Databasebeta

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C2×C11×#13093364 #45656748

order32604
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×#13093364

Splittings

Fitting, socleC2×C11×C13×C19 ⋊ C2×C3
derived, HallC13×C19 ⋊ C22×C3×C11
HallC2×C11×C19×D13 ⋊ C3
HallC11×#10625202 ⋊ C22
HallC11×C13×C19 ⋊ C22×C3
HallC2×C19×D13 ⋊ C3×C11
Hall#10625202 ⋊ C22×C11
HallC2×C11×D13 ⋊ C19⋊C3
HallC11×C19 ⋊ C2×D13⋊C3
HallC11×C13 ⋊ C22×C19⋊C3
HallC2×D13 ⋊ C11×C19⋊C3
SylowC19 ⋊ C2×C11×D13⋊C3
SylowC13 ⋊ C22×C11×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#13093364
commutator, cosocle, hypocenterC13×C19C22×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C13×C19C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5434

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 98);