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C3×C7×C11⋊AGL(1,𝔽5) #17987683

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

Aliases

direct productC3×C7×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C3×C7×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C7×C11 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4×C7
HallC5×C7×C11 ⋊ C3×C4
HallC3×C7×C11 ⋊ AGL(1,𝔽5)
HallC3×C5×C11 ⋊ C4×C7
HallC3×C5×C7 ⋊ Dic11
HallC7×C11 ⋊ C3×AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic11
HallC3×C11 ⋊ C7×AGL(1,𝔽5)
HallC3×C5 ⋊ C7×Dic11
SylowC11 ⋊ C3×C7×AGL(1,𝔽5)
SylowC5 ⋊ C3×C7×Dic11

Subgroups

subgroupG/H
center, hypercenterC3×C7C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11C4
prime radicalC3×C7×D5×C11C2
cosocleD5×C11C2×C3×C7
LCSG ▷ C5×C11
UCSC1 ◁ C3×C7

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)(12,13)(14,15)(16,17)(18,19)(20,21)(23,24,25,26);(11,12,14,16,18,20,21,19,17,15,13)(22,23,26,24,25)

Conjugacy classes & character table

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

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4620, 80);