Finite Group Databasebeta

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C3×C11×#11725131 #44415763

order29172
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×#11725131

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C4
derived, HallC13×C17 ⋊ C3×C4×C11
HallC11×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C11
HallC3×C11×C17 ⋊ #261
HallC3×C11×C13 ⋊ #595
HallC11×C17 ⋊ C3×#261
HallC11×C13 ⋊ C3×#595
HallC3×C17 ⋊ C11×#261
HallC3×C13 ⋊ C11×#595
SylowC17 ⋊ C3×C11×#261
SylowC13 ⋊ C3×C11×#595

Subgroups

subgroupG/H
center, hypercenterC3×C11#11725131
commutator, hypocenterC13×C17C3×C4×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C17C4
prime radicalC3×C11×D221C2
cosocleD221C2×C3×C11
LCSG ▷ C13×C17
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

1947 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 55);