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C11×#1043⋊C3 #15693162

order3300
isoclinismisoclinic class of #1043⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#1043⋊C3
unambiguous semidirect product#1043⋊(C3×C11)
unambiguous semidirect product(C11×#1043)⋊C3

Splittings

Fitting, socle, HallC52×C11 ⋊ C3×C4
derived, SylowC52 ⋊ C3×C4×C11
HallC11×#1043 ⋊ C3
HallC11×C52⋊C3 ⋊ C4
Hall#1043 ⋊ C3×C11
HallC52⋊C3 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC11#1043⋊C3
commutator, hypocenterC52C3×C4×C11
FrattiniC1G
Fitting, socleC52×C11C3×C4
prime radicalC11×(C5⋊D5)⋊C3C2
cosocleC5⋊D5C2×C3×C11
LCSG ▷ C52
UCSC1 ◁ C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 165

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

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

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11×#1043⋊C3, C11×#14523608, C11×#1043⋊ΓL(1,𝔽8), …
maximal normal subgroup ofC7×C11×#1043⋊C3, C121×#1043⋊C3, C112×#1043⋊C3
maximal quotient ofC7×C11×#1043⋊C3, C11×#14523608, C11×#1043⋊ΓL(1,𝔽8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 82);