Q₈×#41×C₁₉ #14561335

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

Q₈×#41×C₁₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁵
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 5 generators on 35 points:

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

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8439, C₁₉×#17509, C₁₉×#17514, …
maximal normal subgroup of	C₁₉×#8439, C₁₉×#17509, C₁₉×#17514, …
maximal quotient of	C₄⋊C₄×#41×C₁₉, Q₈×C₁₉×#117, C₁₉×#34145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2210);

Q8×#41×C19 #14561335

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

Q₈×#41×C₁₉ #14561335