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C11×AGL(1,𝔽5)×#3861 #44568657

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

Aliases

direct productC11×AGL(1,𝔽5)×#3861

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC72×C11×AGL(1,𝔽5) ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC72×AGL(1,𝔽5) ⋊ C3×C11
HallC5×#3861 ⋊ C4×C11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
HallC5×C11 ⋊ C4×#3861
SylowC72 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C4×C11×#3861

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽5)×#3861
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalD5×C11×#3861C2
cosocleC72×D5C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 359);