C₁₉×#3022 #14560879

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

Aliases

direct product

C₁₉×#3022

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 704 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)(20,21,26,31)(22,32,35,44)(23,28,37,43)(24,30,25,29)(27,38,41,34)(33,47,50,46)(36,45,39,42)(40,48,51,49);(20,22)(21,27)(23,33)(24,34)(25,38)(26,35)(28,40)(29,32)(30,44)(31,41)(36,48)(37,50)(39,49)(42,46)(43,51)(45,47);(20,23)(21,28)(22,33)(24,36)(25,39)(26,37)(27,40)(29,42)(30,45)(31,43)(32,46)(34,48)(35,50)(38,49)(41,51)(44,47);(20,24,26,25)(21,29,31,30)(22,34,35,38)(23,36,37,39)(27,32,41,44)(28,42,43,45)(33,48,50,49)(40,46,51,47)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13355, C₁₉×#13356, C₁₉×#13361, …
maximal normal subgroup of	C₁₉×#13355, C₁₉×#13356, C₁₉×#13361, …
maximal quotient of	C₁₉×#18136, C₁₉×#18140, C₁₉×#18146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1754);