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Cayley diagram

C4×D41 #66495

order328
isoclinismisoclinic class of D41
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×D41

Splittings

FittingC4×C41 ⋊ C2
derived, SylowC41 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4D41
commutator, hypocenterC41C2×C4
FrattiniC2C2×D41
FittingC4×C41C2
socle, cosocleC2×C41C22
prime radicalC2×D41C2
LCSG ▷ C41
UCSC1 ◁ C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 164

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×D41, #10620272, #10620296, …
maximal normal subgroup ofC8×D41, #10620272, #10620296, …
maximal quotient ofC8×D41, #10620272, C4×Dic41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(328, 5);