C₁₉×#2988 #14560845

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×#2988

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	C₂×#41×C₁₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#8839, C₁₉×#8840, C₁₉×#8953, …
maximal normal subgroup of	C₁₉×#8839, C₁₉×#8840, C₁₉×#8953, …
maximal quotient of	C₁₉×#20543, C₁₉×#20555, C₁₉×#20569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1720);

C19×#2988 #14560845