Finite Group Databasebeta

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Cayley diagram

C11⋊#95 #66895

order352
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C23

Aliases

unambiguous semidirect productC11⋊#95

Splittings

SylowC11 ⋊ #95

Subgroups

subgroupG/H
center, FrattiniC23C2×D11
commutatorC2×C11C42
FittingC22×C4×C11C2
socle, prime radical, cosocleC23×C11C22
hypercenterC22×C4D11
hypocenterC11#95
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 352

A minimal faithful permutation representation — 2 generators on 23 points:

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

Polycyclic presentation:

2^5,11|a^2=c,b^2=d,b^a=be,f^a=f^10

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10622105, #10622108, #10622175, …
maximal normal subgroup of#10622105, #10622108, #10622175, …
maximal quotient of#10622161, #10622162, #10622164, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 37);