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C11×#15668768 #44568663

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15668768

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC7×C11×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×C11×#3862 ⋊ C4
HallC11×#3862 ⋊ AGL(1,𝔽5)
HallC7×C7⋊AGL(1,𝔽5) ⋊ C3×C11
HallC5×#3862 ⋊ C4×C11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
Hall#3862 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ #10596872
SylowC72 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×#10596872

Subgroups

subgroupG/H
center, hypercenterC11#15668768
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalD5×C11×#3862C2
cosocleC72×D5C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

104 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 365);