Finite Group Databasebeta

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C11×#15688301 #45656702

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

Aliases

direct productC11×#15688301

Splittings

Fitting, socle, HallC11×C13×C19 ⋊ C3×C4
derived, HallC13×C19 ⋊ C3×C4×C11
HallC11×C19⋊#261 ⋊ C3
HallC11×#10625203 ⋊ C4
HallC19⋊#261 ⋊ C3×C11
Hall#10625203 ⋊ C4×C11
HallC11×C19 ⋊ AGL(1,𝔽13)
HallC11×C13 ⋊ (C19⋊C3)⋊C4
SylowC19 ⋊ C11×AGL(1,𝔽13)
SylowC13 ⋊ C11×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC11#15688301
commutator, hypocenterC13×C19C3×C4×C11
FrattiniC1G
Fitting, socleC11×C13×C19C3×C4
prime radicalC11×#13093365C2
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32604, 52);