C₂×C₄×Q₁₆×C₁₉ #14560795

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₄×Q₁₆×C₁₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle, prime radical	C₂³×C₁₉	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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×#8946, C₁₉×#8950, C₁₉×#9656, …
maximal normal subgroup of	C₁₉×#8946, C₁₉×#8950, C₁₉×#9656, …
maximal quotient of	C₂×C₈×Q₁₆×C₁₉, C₂×C₁₉×#1584, C₂×C₁₉×#1591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1670);

C2×C4×Q16×C19 #14560795