C₁₉×#2846 #14560703

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁹

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

3422 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 4 generators on 31 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1578);