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Cayley diagram

C11×D23 #92782

order506
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D23

Splittings

Fitting, socle, HallC11×C23 ⋊ C2
derived, SylowC23 ⋊ C2×C11

Subgroups

subgroupG/H
center, hypercenterC11D23
commutator, cosocle, hypocenterC23C2×C11
FrattiniC1G
Fitting, socleC11×C23C2
LCSG ▷ C23
UCSC1 ◁ C11

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 253

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D23, C2×C11×D23, C3×C11×D23, …
maximal normal subgroup ofD11×D23, C2×C11×D23, C3×C11×D23, …
maximal quotient ofC11×Dic23, C2×C11×D23, C3×C11×D23, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(506, 4);