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C3×C11×#1181 #16838569

order3828
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×#1181

Splittings

Fitting, socle, HallC3×C11×C29 ⋊ C4
derived, SylowC29 ⋊ C3×C4×C11
HallC11×C29 ⋊ C3×C4
HallC3×C29 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11#1181
commutator, hypocenterC29C3×C4×C11
FrattiniC1G
Fitting, socleC3×C11×C29C4
prime radicalC3×C11×D29C2
cosocleD29C2×C3×C11
LCSG ▷ C29
UCSC1 ◁ C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 957

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14)(16,17,18,20)(19,22,23,29)(21,26,27,25)(24,31,32,39)(28,35,36,37)(30,38,33,34)(40,42,43,41);(15,16,19,24,33,29,37,31,40,42,38,26,17,21,28,36,27,20,25,34,41,43,39,35,22,30,32,23,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×C11×#1181, C32×C11×#1181, C3×C11×C3⋊#1181, …
maximal normal subgroup ofC9×C11×#1181, C32×C11×#1181, C3×C11⋊C5×#1181, …
maximal quotient ofC9×C11×#1181, C32×C11×#1181, C3×C11×C3⋊#1181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3828, 10);