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C3×C7×C11×AGL(1,𝔽5) #17987682

order4620
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC3×C5×C7×C11 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C7×C11
HallC5×C7×C11 ⋊ C3×C4
HallC3×C5×C11 ⋊ C4×C7
HallC3×C5×C7 ⋊ C4×C11
HallC5×C11 ⋊ C3×C4×C7
HallC5×C7 ⋊ C3×C4×C11
HallC3×C5 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11C4
prime radicalC3×C7×D5×C11C2
cosocleD5C2×C3×C7×C11
LCSG ▷ C5
UCSC1 ◁ C3×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1155

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21)(23,24,25,26);(22,23,24,26,25)

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×AGL(1,𝔽5)×C7⋊C9, C7×C9×C11×AGL(1,𝔽5), C3×C11×AGL(1,𝔽5)×ΓL(1,𝔽8), …
maximal normal subgroup ofC11×AGL(1,𝔽5)×C7⋊C9, C7×C9×C11×AGL(1,𝔽5), C3×C11×AGL(1,𝔽5)×ΓL(1,𝔽8), …
maximal quotient ofC7×C9×C11×AGL(1,𝔽5), C32×C7×C11×AGL(1,𝔽5), C3×C7×C11×ΓL(1,𝔽16), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 79);