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C3×C11×#1035 #15693100

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

Aliases

direct productC3×C11×#1035

Splittings

Fitting, HallC3×C11×C25 ⋊ C4
derived, SylowC25 ⋊ C3×C4×C11
HallC11×C25 ⋊ C3×C4
HallC3×C25 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11#1035
commutator, hypocenterC25C3×C4×C11
FrattiniC5C3×C11×AGL(1,𝔽5)
FittingC3×C11×C25C4
socleC3×C5×C11AGL(1,𝔽5)
prime radicalC3×C11×D25C2
cosocleD25C2×C3×C11
LCSG ▷ C25
UCSC1 ◁ C3×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)(4,5,6,7,8,9,10,11,12,13,14)(16,18,19,24)(17,22,23,34)(20,28,29,33)(21,31,32,25)(26,36,37,39)(27,30,35,38);(15,16,20,30,27,17,21,18,25,36,22,33,26,37,28,34,39,31,24,32,23,35,38,29,19)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊#1035, C11×ΓL(1,𝔽8)×#1035, C3×C7×C11×#1035, …
maximal normal subgroup ofC3×C7×C11×#1035, C3×#1035×C121, C3×C112×#1035
maximal quotient ofC11×ΓL(1,𝔽8)⋊#1035, C11×ΓL(1,𝔽8)×#1035, C3×C7×C11×#1035, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 20);