Finite Group Databasebeta

← Prev (#66810) Next (#66812) →

Cayley diagram

C2×Dic43 #66811

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

Aliases

direct productC2×Dic43
unambiguous semidirect product(C2×C43)⋊C4

Splittings

derived, SylowC43 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22D43
commutator, hypocenterC43C2×C4
FrattiniC2C2×D43
Fitting, socle, prime radicalC22×C43C2
cosocleC2×C43C22
LCSG ▷ C43
UCSC1 ◁ C22

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 344

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2)(3,4,5,6)(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)(48,49);(1,2)(7,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×Dic43, Dic43⋊C4, C4⋊Dic43, …
maximal normal subgroup ofC4×Dic43, Dic43⋊C4, C4⋊Dic43, …
maximal quotient ofC2×C43⋊C8, #10621877, C4×Dic43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(344, 6);