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Cayley diagram

C4×Dic13 #6100

order208
isoclinismisoclinic class of D13
automorphismAut(G) = #120×AGL(1,𝔽13) (order 4992) · Inn(G) = D13 · Out(G) = C2×C3×#120
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

direct productC4×Dic13

Splittings

derived, SylowC13 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2×C4D13
commutator, hypocenterC13C42
FrattiniC22C2×D13
FittingC2×C4×C13C2
socle, prime radical, cosocleC22×C13C22
LCSG ▷ C13
UCSC1 ◁ C2×C4

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×Dic13, #88054, #88055, …
maximal normal subgroup ofC8×Dic13, #88054, #88055, …
maximal quotient ofC4×#1055, #88043, C8×Dic13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 11);