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C2×D147 #10596866

order588
isoclinismisoclinic class of D147
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD294
direct productC2×D147
unambiguous semidirect product(C2×C3)⋊D49
unambiguous semidirect product(C2×C49)⋊D3

Splittings

FittingC2×C3×C49 ⋊ C2
derived, HallC3×C49 ⋊ C22
SylowC49 ⋊ C2×D3
SylowC3 ⋊ C2×D49

Subgroups

subgroupG/H
center, hypercenterC2D147
commutator, cosocle, hypocenterC3×C49C22
FrattiniC7C2×D21
FittingC2×C3×C49C2
socleC2×C3×C7D7
LCSG ▷ C3×C49
UCSC1 ◁ C2

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 294

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(4,5)(7,54)(8,53)(9,52)(10,51)(11,50)(12,49)(13,48)(14,47)(15,46)(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD147⋊C4, #11924100, #11924103, …
maximal normal subgroup ofD147⋊C4, #11924100, #11924103, …
maximal quotient ofDic294, C4×D147, D588, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(588, 14);