C₁₉×#2656 #14560513

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#2656

Subgroups

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

804 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 232 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)(20,21,22,23)(28,29)(30,32)(31,33)(34,35);(24,25,26,27)(28,29,31,33)(30,32,35,34);(20,21)(22,23)(24,25)(26,27)(28,29)(30,34)(31,33)(32,35);(28,30)(29,32)(31,35)(33,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9962, C₁₉×#9964, C₁₉×#9968, …
maximal normal subgroup of	C₁₉×#9962, C₁₉×#9964, C₁₉×#9968, …
maximal quotient of	C₁₉×#14271, C₁₉×#14321, C₁₉×#14322, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1388);