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Cayley diagram

C4×D47 #67338

order376
isoclinismisoclinic class of D47
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×D47

Splittings

FittingC4×C47 ⋊ C2
derived, SylowC47 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4D47
commutator, hypocenterC47C2×C4
FrattiniC2C2×D47
FittingC4×C47C2
socle, cosocleC2×C47C22
prime radicalC2×D47C2
LCSG ▷ C47
UCSC1 ◁ C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 188

A minimal faithful permutation representation — 2 generators on 51 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)(44,45)(46,47);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(48,49,50,51)

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×D47, #10625324, C2×C4×D47, …
maximal normal subgroup ofC8×D47, #10625324, C2×C4×D47, …
maximal quotient ofC8×D47, #10625324, C4×Dic47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(376, 4);