C₂²×C₁₉×2₋¹⁺⁴ #14561449

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₉ · Schur multiplier (H₂) = C₂¹⁴

Aliases

direct product

C₂²×C₁₉×2₋¹⁺⁴

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

5872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 6 generators on 39 points:

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

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#20587, C₁₉×#20593, C₁₉×#20603, …
maximal normal subgroup of	C₁₉×#20587, C₁₉×#20593, C₁₉×#20603, …
maximal quotient of	C₂²×C₁₉×#519, C₂²×C₁₉×#520, C₂×C₄×C₁₉×2₋¹⁺⁴, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2324);

C22×C19×2−1+4 #14561449