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Cayley diagram

C22×D43 #66816

order344
isoclinismisoclinic class of D43
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC22×D43
unambiguous semidirect productC43⋊C23
unambiguous semidirect product(C2×C43)⋊C22

Splittings

Fitting, socleC22×C43 ⋊ C2
derived, SylowC43 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22D43
commutator, cosocle, hypocenterC43C23
FrattiniC1G
Fitting, socleC22×C43C2
LCSG ▷ C43
UCSC1 ◁ C22

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 172

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2)(3,4)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47);(3,4)(5,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7);(1,2)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D43)⋊C4, C2×C4×D43, C2×D172, …
maximal normal subgroup of(C2×D43)⋊C4, C2×C4×D43, C2×D172, …
maximal quotient ofC2×Dic86, C2×C4×D43, C2×D172, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(344, 11);