C₁₉×#3020 #14560877

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#3020

Subgroups

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

698 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30)(23,27)(24,36)(25,28)(26,32)(29,39)(31,47)(33,44)(34,45)(35,42)(37,41)(38,43)(40,48)(46,49)(50,51);(20,22)(21,26)(23,31)(24,37)(25,33)(27,40)(28,41)(29,44)(30,36)(32,39)(34,50)(35,49)(38,48)(42,51)(43,46)(45,47);(20,23,25,35)(21,27,28,42)(22,31,33,49)(24,38,39,34)(26,40,41,51)(29,45,36,43)(30,46,44,47)(32,50,37,48);(21,28)(26,41)(27,42)(29,36)(30,44)(40,51)(43,45)(46,47)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#23874, C₁₉×#23875, C₁₉×#23893, …
maximal normal subgroup of	C₁₉×#23874, C₁₉×#23875, C₁₉×#23893, …
maximal quotient of	C₁₉×#18134, C₁₉×#18139, C₁₉×#18142, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1752);