C₁₉×#2982 #14560839

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×#2982

Subgroups

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

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#8836, C₁₉×#8958, C₁₉×#8960, …
maximal normal subgroup of	C₁₉×#8836, C₁₉×#8958, C₁₉×#8960, …
maximal quotient of	C₁₉×#20533, C₁₉×#20569, C₁₉×#21818, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1714);

C19×#2982 #14560839