C₁₉×#2621 #14560478

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#2621

Subgroups

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

528 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9195, C₁₉×#9196, C₁₉×#11694, …
maximal normal subgroup of	C₁₉×#9195, C₁₉×#9196, C₁₉×#11694, …
maximal quotient of	C₁₉×#14258, C₁₉×#14261, C₁₉×#14274, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1353);