C₁₉×#2972 #14560829

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×#2972

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	C₂²×D₄×C₁₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 608

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)(20,21)(22,26)(23,25)(24,27)(28,29,30,32,31,33,34,35);(20,22)(21,24)(23,27)(25,26);(22,27)(24,26);(21,25)(24,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#8835, C₁₉×#8851, C₁₉×#8957, …
maximal normal subgroup of	C₁₉×#8835, C₁₉×#8851, C₁₉×#8957, …
maximal quotient of	C₁₉×#20523, C₁₉×#20533, C₁₉×#20555, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1704);

C19×#2972 #14560829