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C17×C11⋊AGL(1,𝔽5) #16836682

order3740
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C17×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C11×C17 ⋊ C4
derived, HallC5×C11 ⋊ C4×C17
HallC11×C17 ⋊ AGL(1,𝔽5)
HallC5×C17 ⋊ Dic11
SylowC11 ⋊ C17×AGL(1,𝔽5)
SylowC5 ⋊ C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC17C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C17
FrattiniC1G
Fitting, socleC5×C11×C17C4
prime radicalD5×C11×C17C2
cosocleD5×C11C2×C17
LCSG ▷ C5×C11
UCSC1 ◁ C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 935

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(21,22)(23,24)(25,26)(27,28)(30,31,32,33);(18,19,21,23,25,27,28,26,24,22,20)(29,30,33,31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C17×C11⋊AGL(1,𝔽5), C17×C3⋊(C11⋊AGL(1,𝔽5)), C17×C11⋊#1035, …
maximal normal subgroup ofC3×C17×C11⋊AGL(1,𝔽5), C17×(C11⋊C5)⋊AGL(1,𝔽5), C5×C17×C11⋊AGL(1,𝔽5), …
maximal quotient ofC3×C17×C11⋊AGL(1,𝔽5), C17×C3⋊(C11⋊AGL(1,𝔽5)), C17×C11⋊#1035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 28);