C₂²×C₃₁×C₁₃⋊C₃ #18012858

order	4836
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂²×C₃₁×C₁₃⋊C₃

Splittings

Fitting, socle, Hall	C₂²×C₁₃×C₃₁ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₂²×C₃×C₃₁
Hall	C₁₃×C₃₁ ⋊ C₂²×C₃
Hall	C₂²×C₁₃ ⋊ C₃×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₃₁	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 1612

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2)(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)(37,38,40)(39,42,45)(41,44,43)(46,48,47);(3,4)(36,37,39,38,41,45,42,46,48,40,43,47,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂²×C₁₃⋊C₃×C₃₁⋊C₃, A₄×C₃₁×C₁₃⋊C₃, C₁₃⋊C₃×C₂²⋊(C₃₁⋊C₃), …
maximal normal subgroup of	C₂²×C₁₃⋊C₃×C₃₁⋊C₃, A₄×C₃₁×C₁₃⋊C₃, C₁₃⋊C₃×C₂²⋊(C₃₁⋊C₃), …
maximal quotient of	C₂²×C₃₁×C₁₃⋊C₉, C₂×D₃×C₃₁×C₁₃⋊C₃, C₂²×C₃×C₃₁×C₁₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4836, 62);

C22×C31×C13⋊C3 #18012858