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C11×C17×C3⋊#261 #44415781

order29172
automorphism?
homologyAbelianization (H1) = C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×C3⋊#261
unambiguous semidirect productC3⋊(C11×C17×#261)

Splittings

Fitting, socle, HallC3×C11×C13×C17 ⋊ C4
derived, HallC3×C13 ⋊ C4×C11×C17
HallC11×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ C4×C11
HallC3×C11×C17 ⋊ #261
HallC3×C11×C13 ⋊ C4×C17
HallC13×C17 ⋊ C11×Dic3
HallC11×C13 ⋊ Dic3×C17
HallC3×C17 ⋊ C11×#261
HallC3×C11 ⋊ C17×#261
SylowC13 ⋊ C11×Dic3×C17
SylowC3 ⋊ C11×C17×#261

Subgroups

subgroupG/H
center, hypercenterC11×C17C3⋊#261
commutator, hypocenterC3×C13C4×C11×C17
FrattiniC1G
Fitting, socleC3×C11×C13×C17C4
prime radicalC3×C11×C17×D13C2
cosocleC3×D13C2×C11×C17
LCSG ▷ C3×C13
UCSC1 ◁ C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7293

Conjugacy classes & character table

2805 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29172, 73);