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Cayley diagram

D132 #63157

order264
isoclinismisoclinic class of Dic66
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD132
unambiguous semidirect productC4⋊D33

Splittings

FittingC3×C4×C11 ⋊ C2
HallC3×C11 ⋊ D4
SylowC11 ⋊ D12
SylowC3 ⋊ D44

Subgroups

subgroupG/H
center, FrattiniC2C2×D33
commutator, socle, cosocleC2×C3×C11C22
FittingC3×C4×C11C2
hypercenterC4D33
hypocenterC3×C11D4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18);(2,4)(6,7)(9,18)(10,17)(11,16)(12,15)(13,14)

Polycyclic presentation:

2^3,3,11|b^2=c,b^a=bc,d^a=d^2,e^a=e^10

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10587142, #10587143, #10587147, …
maximal normal subgroup of#10587142, #10587143, #10587147, …
maximal quotient of#10587195, D264, Dic132, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 25);