C₃×C₁₁⋊C₃₂ #11760465

order	1056
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₁⋊C₃₂
unambiguous semidirect product	C₁₁⋊(C₃×C₃₂)

Splittings

derived, Sylow	C₁₁ ⋊ C₃×C₃₂
Hall	C₃×C₁₁ ⋊ C₃₂

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₆	D₁₁
commutator, hypocenter	C₁₁	C₃×C₃₂
Frattini	C₁₆	C₃×D₁₁
Fitting	C₃×C₁₁×C₁₆	C₂
socle, prime radical	C₂×C₃×C₁₁	C₁₆
cosocle	C₁₁×C₁₆	C₂×C₃
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₁₆

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1056

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

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

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 2);

C3×C11⋊C32 #11760465