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Cayley diagram

C2×Dic59 #90893

order472
isoclinismisoclinic class of D59
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC2×Dic59
unambiguous semidirect product(C2×C59)⋊C4

Splittings

derived, SylowC59 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22D59
commutator, hypocenterC59C2×C4
FrattiniC2C2×D59
Fitting, socle, prime radicalC22×C59C2
cosocleC2×C59C22
LCSG ▷ C59
UCSC1 ◁ C22

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 472

A minimal faithful permutation representation — 2 generators on 65 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)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65);(1,2)(7,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9)

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×Dic59, Dic59⋊C4, C4⋊Dic59, …
maximal normal subgroup ofC4×Dic59, Dic59⋊C4, C4⋊Dic59, …
maximal quotient ofC2×C59⋊C8, #11745664, C4×Dic59, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(472, 6);