C₂₉×D₃₃ #14274285

order	1914
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₃₃
unambiguous semidirect product	C₃⋊(D₁₁×C₂₉)
unambiguous semidirect product	C₁₁⋊(D₃×C₂₉)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₂₉ ⋊ C₂
derived, Hall	C₃×C₁₁ ⋊ C₂×C₂₉
Hall	C₁₁×C₂₉ ⋊ D₃
Hall	C₃×C₂₉ ⋊ D₁₁
Sylow	C₁₁ ⋊ D₃×C₂₉
Sylow	C₃ ⋊ D₁₁×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₂₉	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 957

A minimal faithful permutation representation — 2 generators on 43 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);(31,32)(34,43)(35,42)(36,41)(37,40)(38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₉×D₃₃, D₃×D₁₁×C₂₉, D₃₃⋊D₂₉, …
maximal normal subgroup of	D₂₉×D₃₃, D₃×D₁₁×C₂₉, D₃₃⋊D₂₉, …
maximal quotient of	C₂₉×Dic₃₃, C₂×C₂₉×D₃₃, C₇×C₂₉×D₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1914, 6);

C29×D33 #14274285