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C₁₉×#2358 #14560215

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 608

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

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12958, C₁₉×#13041, C₂×C₁₉×#2358, …
maximal normal subgroup of	C₁₉×#12958, C₁₉×#13041, C₂×C₁₉×#2358, …
maximal quotient of	C₂²⋊C₄²×C₁₉, C₁₉×#13813, C₁₉×#13814, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1090);