C₁₉×#2363 #14560220

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#2363

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

688 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)(21,23)(24,25,27,26)(28,29,32,31)(30,33,35,34);(24,26,27,25)(29,31)(33,34);(20,21)(22,23)(28,30,32,35)(29,33,31,34);(28,31,32,29)(30,34,35,33)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#22857, C₁₉×#22860, C₁₉×#22865, …
maximal normal subgroup of	C₁₉×#22857, C₁₉×#22860, C₁₉×#22865, …
maximal quotient of	C₁₉×#13801, C₁₉×#13816, C₁₉×#13818, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1095);

C19×#2363 #14560220

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2363 #14560220