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Cayley diagram

C4×D43 #66809

order344
isoclinismisoclinic class of D43
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×D43

Splittings

FittingC4×C43 ⋊ C2
derived, SylowC43 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4D43
commutator, hypocenterC43C2×C4
FrattiniC2C2×D43
FittingC4×C43C2
socle, cosocleC2×C43C22
prime radicalC2×D43C2
LCSG ▷ C43
UCSC1 ◁ C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×D43, #10621872, C2×C4×D43, …
maximal normal subgroup ofC8×D43, #10621872, C2×C4×D43, …
maximal quotient ofC8×D43, #10621872, C4×Dic43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(344, 4);