C₂²×C₁₃×C₁₉⋊C₃ #15688334

order	2964
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂²×C₁₃×C₁₉⋊C₃

Splittings

Fitting, socle, Hall	C₂²×C₁₃×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂²×C₃×C₁₃
Hall	C₁₃×C₁₉ ⋊ C₂²×C₃
Hall	C₂²×C₁₉ ⋊ C₃×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₁₃	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₁₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 988

A minimal faithful permutation representation — 2 generators on 36 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×D₅×C₁₃×C₁₉⋊C₃, C₂²×C₅×C₁₃×C₁₉⋊C₃, C₂×C₁₃×#11716325, …
maximal normal subgroup of	C₂²×C₅×C₁₃×C₁₉⋊C₃, C₂²×C₇×C₁₃×C₁₉⋊C₃, C₂²×C₁₁×C₁₃×C₁₉⋊C₃, …
maximal quotient of	C₂×D₅×C₁₃×C₁₉⋊C₃, C₂²×C₅×C₁₃×C₁₉⋊C₃, C₂×C₁₃×#11716325, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2964, 61);

C22×C13×C19⋊C3 #15688334