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C11×#15688304 #45656705

order32604
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15688304

Splittings

Fitting, socle, HallC11×C13×C19 ⋊ C3×C4
derived, HallC13×C19 ⋊ C3×C4×C11
HallC11×C19⋊#261 ⋊ C3
HallC11×C19×C13⋊C3 ⋊ C4
HallC19⋊#261 ⋊ C3×C11
HallC19×C13⋊C3 ⋊ C4×C11
HallC11×C13⋊C3 ⋊ Dic19
HallC11×C19 ⋊ AGL(1,𝔽13)
HallC11×C13 ⋊ C3×Dic19
HallC13⋊C3 ⋊ C11×Dic19
SylowC19 ⋊ C11×AGL(1,𝔽13)
SylowC13 ⋊ C3×C11×Dic19

Subgroups

subgroupG/H
center, hypercenterC11#15688304
commutator, hypocenterC13×C19C3×C4×C11
FrattiniC1G
Fitting, socleC11×C13×C19C3×C4
prime radicalC11×C19×D13⋊C3C2
cosocleC19×D13C2×C3×C11
LCSG ▷ C13×C19
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2717

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 55);