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C11×C3⋊#1035 #15693102

order3300
isoclinismisoclinic class of C3⋊#1035
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊#1035
unambiguous semidirect productC3⋊(C11×#1035)

Splittings

Fitting, HallC3×C11×C25 ⋊ C4
derived, HallC3×C25 ⋊ C4×C11
HallC11×C25 ⋊ Dic3
HallC3×C11 ⋊ #1035
SylowC25 ⋊ C11×Dic3
SylowC3 ⋊ C11×#1035

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#1035
commutator, hypocenterC3×C25C4×C11
FrattiniC5C11×ΓL(1,𝔽16)
FittingC3×C11×C25C4
socleC3×C5×C11AGL(1,𝔽5)
prime radicalC3×C11×D25C2
cosocleC3×D25C2×C11
LCSG ▷ C3×C25
UCSC1 ◁ C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 825

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,15,16,22)(14,19,20,21)(17,26,27,25)(18,30,31,36)(23,29,32,24)(28,35,34,33)(38,39);(12,33,29,30,31,21,13,34,15,25,20,32,17,27,23,14,26,22,28,16,19,18,36,24,35)(37,38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C11×C3⋊#1035, C11×C3⋊(C7⋊#1035), C121×C3⋊#1035, …
maximal normal subgroup ofC7×C11×C3⋊#1035, C121×C3⋊#1035, C112×C3⋊#1035
maximal quotient ofC7×C11×C3⋊#1035, C11×C3⋊(C7⋊#1035), C121×C3⋊#1035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 22);