C₁₉×#2501 #14560358

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#2501

Subgroups

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

708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 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)(21,22)(25,26)(28,29,32,34)(30,31,33,35);(20,21,23,22)(24,25,27,26)(28,30)(29,31)(32,33)(34,35);(24,25,27,26)(28,31)(29,33)(30,34)(32,35);(20,22,23,21)(24,26,27,25)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9464, C₁₉×#9952, C₁₉×#9960, …
maximal normal subgroup of	C₁₉×#9464, C₁₉×#9952, C₁₉×#9960, …
maximal quotient of	C₁₉×#13880, C₁₉×#13904, C₁₉×#13996, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1233);