C₁₉×#2929 #14560786

order	2432
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2929

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂³
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₁₉×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#8238, C₁₉×#8239, C₁₉×#8240, …
maximal normal subgroup of	C₁₉×#8238, C₁₉×#8239, C₁₉×#8240, …
maximal quotient of	C₁₉×#17900, C₁₉×#17901, C₁₉×#17902, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1661);

C19×#2929 #14560786