C₁₉×#3407 #14561264

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#3407

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂⁴
commutator	C₂	C₂³×C₈×C₁₉
Frattini, cosocle	C₈	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂³×C₈
prime radical	C₂×#41×C₁₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,28,24,29,33,41,25,27,34,39,35,40,45,49)(22,26,31,37,32,38,44,48,30,36,42,46,43,47,50,51);(20,22)(21,26)(23,31)(24,32)(25,30)(27,36)(28,37)(29,38)(33,44)(34,42)(35,43)(39,46)(40,47)(41,48)(45,50)(49,51);(22,30)(26,36)(31,42)(32,43)(37,46)(38,47)(44,50)(48,51);(21,27)(26,36)(28,39)(29,40)(37,46)(38,47)(41,49)(48,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#12618, C₁₉×#12833, C₁₉×#12915, …
maximal normal subgroup of	C₁₉×#12618, C₁₉×#12833, C₁₉×#12915, …
maximal quotient of	C₁₉×#33324, C₁₉×#33326, C₁₉×#33333, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2139);

C19×#3407 #14561264