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C11×#66776 #16836680

order3740
isoclinismisoclinic class of #66776
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#66776

Splittings

Fitting, socle, HallC5×C11×C17 ⋊ C4
derived, HallC5×C17 ⋊ C4×C11
HallC11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11 ⋊ #595
SylowC17 ⋊ C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×#595

Subgroups

subgroupG/H
center, hypercenterC11#66776
commutator, hypocenterC5×C17C4×C11
FrattiniC1G
Fitting, socleC5×C11×C17C4
prime radicalC11×D85C2
cosocleD85C2×C11
LCSG ▷ C5×C17
UCSC1 ◁ C11

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)(13,14,15,17)(16,19,20,24)(18,23,21,22)(25,27,28,26)(30,31,32,33);(12,13,16,21,17,22,26,28,24,19,25,27,23,14,18,20,15)(29,30,33,31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C11×#66776, C11×C3⋊#66776, C11×#13133324, …
maximal normal subgroup ofC3×C11×#66776, C11⋊C5×#66776, C5×C11×#66776, …
maximal quotient ofC3×C11×#66776, C11×C3⋊#66776, C11×#13133324, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 26);