C₂×C₁₉×#405 #14560729

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₁₉×#405

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₁₉	C₂²
commutator	C₂	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂⁴×C₁₉	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₉ ◁ G

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1216

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);(7,8,10,13,11,14,17,20)(9,12,16,19,15,18,21,22);(3,4,5,6)(7,9)(8,12)(10,16)(11,15)(13,19)(14,18)(17,21)(20,22);(9,15)(12,18)(16,21)(19,22)

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#8156, C₁₉×#8157, C₁₉×#8601, …
maximal normal subgroup of	C₁₉×#8156, C₁₉×#8157, C₁₉×#8601, …
maximal quotient of	C₂×C₈×M₁₆×C₁₉, C₂×C₁₉×#1450, C₂×C₁₉×#1451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1604);

C2×C19×#405 #14560729