C₃₇×C₁₃⋊C₃ #13089647

order	1443
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₇×C₁₃⋊C₃
unambiguous semidirect product	C₁₃⋊(C₃×C₃₇)

Splittings

Fitting, socle, Hall	C₁₃×C₃₇ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₇	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 481

A minimal faithful permutation representation — 2 generators on 50 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×C₁₃⋊C₃, C₁₃⋊C₃×D₃₇, C₃₇×D₁₃⋊C₃, …
maximal normal subgroup of	C₂×C₃₇×C₁₃⋊C₃, C₁₃⋊C₃×D₃₇, C₃₇×D₁₃⋊C₃, …
maximal quotient of	C₂×C₃₇×C₁₃⋊C₃, C₃₇×C₁₃⋊C₉, C₃×C₃₇×C₁₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1443, 1);

C37×C13⋊C3 #13089647