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Cayley diagram

C2×Dic47 #67340

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

Aliases

direct productC2×Dic47
unambiguous semidirect product(C2×C47)⋊C4

Splittings

derived, SylowC47 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22D47
commutator, hypocenterC47C2×C4
FrattiniC2C2×D47
Fitting, socle, prime radicalC22×C47C2
cosocleC2×C47C22
LCSG ▷ C47
UCSC1 ◁ C22

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 376

A minimal faithful permutation representation — 2 generators on 53 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)(50,51)(52,53);(1,2)(7,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9)

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×Dic47, Dic47⋊C4, C4⋊Dic47, …
maximal normal subgroup ofC4×Dic47, Dic47⋊C4, C4⋊Dic47, …
maximal quotient ofC2×C47⋊C8, #10625329, C4×Dic47, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(376, 6);