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Cayley diagram

C2×D123 #92455

order492
isoclinismisoclinic class of D123
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD246
direct productC2×D123
unambiguous semidirect product(C2×C3)⋊D41
unambiguous semidirect product(C2×C41)⋊D3

Splittings

Fitting, socleC2×C3×C41 ⋊ C2
derived, HallC3×C41 ⋊ C22
SylowC41 ⋊ C2×D3
SylowC3 ⋊ C2×D41

Subgroups

subgroupG/H
center, hypercenterC2D123
commutator, cosocle, hypocenterC3×C41C22
FrattiniC1G
Fitting, socleC2×C3×C41C2
LCSG ▷ C3×C41
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 246

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2)(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);(4,5)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11758295, #11758297, #11758298, …
maximal normal subgroup of#11758295, #11758297, #11758298, …
maximal quotient ofDic246, C4×D123, D492, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(492, 11);