C₂×C₂₉×C₁₉⋊C₃ #15693248

order	3306
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₂₉×C₁₉⋊C₃
unambiguous semidirect product	(C₂×C₁₉)⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂×C₁₉×C₂₉)⋊C₃

Splittings

Fitting, socle, Hall	C₂×C₁₉×C₂₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂×C₃×C₂₉
Hall	C₁₉×C₂₉ ⋊ C₂×C₃
Hall	C₂×C₁₉ ⋊ C₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₂₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₂₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 1102

A minimal faithful permutation representation — 2 generators on 50 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)(33,34,36)(35,38,39)(37,41,40)(42,46,44)(43,47,45)(48,50,49);(32,33,35,39,44,49,46,34,37,42,47,36,40,45,38,43,48,50,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₅×C₂₉×C₁₉⋊C₃, D₅×C₂₉×C₁₉⋊C₃, C₂×C₇×C₂₉×C₁₉⋊C₃, …
maximal normal subgroup of	C₂×C₅×C₂₉×C₁₉⋊C₃, C₂×C₇×C₂₉×C₁₉⋊C₃, C₂×C₁₉⋊C₃×C₂₉⋊C₇, …
maximal quotient of	C₂×C₅×C₂₉×C₁₉⋊C₃, D₅×C₂₉×C₁₉⋊C₃, C₂×C₇×C₂₉×C₁₉⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3306, 2);

C2×C29×C19⋊C3 #15693248