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C17×Dic11⋊C5 #16836657

order3740
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C17)
unambiguous semidirect product(C11⋊C5)⋊(C4×C17)
unambiguous semidirect product(C17×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C17
HallC17×C11⋊C5 ⋊ C4
HallC17×Dic11 ⋊ C5
HallC11×C17 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C17
HallDic11 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C17
FrattiniC2C17×AGL(1,𝔽11)
Fitting, socleC2×C11×C17C2×C5
prime radicalC2×C17×C11⋊C5C2
cosocleC2×C11C2×C5×C17
LCSG ▷ C11
UCSC1 ◁ C2×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 748

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C17×Dic11⋊C5, C17×C3⋊(Dic11⋊C5), C5×C17×Dic11⋊C5, …
maximal normal subgroup ofC3×C17×Dic11⋊C5, C5×C17×Dic11⋊C5, C7×C17×Dic11⋊C5
maximal quotient ofC3×C17×Dic11⋊C5, C17×C3⋊(Dic11⋊C5), C17×Dic11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 3);