C₂³×Q₁₆×C₁₉ #14561433

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂³×Q₁₆×C₁₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 5 generators on 41 points:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#11024, C₁₉×#11029, C₁₉×#12732, …
maximal normal subgroup of	C₁₉×#11024, C₁₉×#11029, C₁₉×#12732, …
maximal quotient of	C₂³×C₁₉×#103, C₂³×C₁₉×#107, C₂²×C₄×Q₁₆×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2308);

C23×Q16×C19 #14561433