Finite Group Databasebeta

← Prev (#44568666) Next (#44568668) →

C11×#15668766 #44568667

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C7

Aliases

direct productC11×#15668766

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC11×C7⋊(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 ⋊ #10596875
SylowC72 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×#10596875

Subgroups

subgroupG/H
center, hypercenterC11#15668766
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalD5×C11×#3862C2
cosocleC72×D5C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 369);