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Cayley diagram

C2×D124 #92494

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

Aliases

direct productC2×D124

Splittings

FittingC2×C4×C31 ⋊ C2
SylowC31 ⋊ C2×D4

Subgroups

subgroupG/H
centerC22C2×D31
commutator, cosocleC2×C31C23
FrattiniC2C22×D31
FittingC2×C4×C31C2
socleC22×C31C22
hypercenterC2×C4D31
hypocenterC31C2×D4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 248

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11758397, #11758409, #11758411, …
maximal normal subgroup of#11758397, #11758409, #11758411, …
maximal quotient of#11758446, C4×D124, #11758451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 29);