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Cayley diagram

C2×Dic62 #92492

order496
isoclinismisoclinic class of Dic62
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic62
unambiguous semidirect product(C2×C31)⋊Q8

Splittings

SylowC31 ⋊ C2×Q8

Subgroups

subgroupG/H
centerC22C2×D31
commutator, cosocleC2×C31C23
FrattiniC2C22×D31
FittingC2×C4×C31C2
socle, prime radicalC22×C31C22
hypercenterC2×C4D31
hypocenterC31C2×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 496

A minimal faithful permutation representation — 3 generators on 41 points:

(3,5,6,10)(4,7,8,9)(11,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13);(1,2)(3,4,6,8)(5,9,10,7)(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)

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11758398, #11758404, #11758412, …
maximal normal subgroup of#11758398, #11758404, #11758412, …
maximal quotient ofC4×Dic62, #11758446, #11758447, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 27);