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C32×C11×AGL(1,𝔽5) #14520448

order1980
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC32×C5×C11 ⋊ C4
derived, SylowC5 ⋊ C32×C4×C11
HallC5×C11 ⋊ C32×C4
HallC32×C5 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC32×C11AGL(1,𝔽5)
commutator, hypocenterC5C32×C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11C4
prime radicalC32×D5×C11C2
cosocleD5C2×C32×C11
LCSG ▷ C5
UCSC1 ◁ C32×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 495

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3)(7,8,9,10,11,12,13,14,15,16,17)(19,20,21,22);(4,5,6)(18,19,20,22,21)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C11×AGL(1,𝔽5)×ΓL(1,𝔽8), C32×C7×C11×AGL(1,𝔽5), …
maximal normal subgroup ofC32×C7×C11×AGL(1,𝔽5), C32×AGL(1,𝔽5)×C121, C32×C112×AGL(1,𝔽5), …
maximal quotient ofC3×C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×C11×AGL(1,𝔽5)×ΓL(1,𝔽8), C32×C7×C11×AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 73);