C₂×C₁₉×#397 #14560247

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₉×#397

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9025, C₁₉×#9028, C₁₉×#9918, …
maximal normal subgroup of	C₁₉×#9025, C₁₉×#9028, C₁₉×#9918, …
maximal quotient of	C₂×C₁₉×#1439, C₂×C₁₉×#1440, C₂×C₁₉×#1442, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1122);

C2×C19×#397 #14560247

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#397 #14560247