C₁₉×#3025 #14560882

order	2432
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#3025

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₉
socle	C₂×C₁₉	C₂×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 766 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) = 35
transitive degree	μ_t(G) = 304

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)(25,31)(32,35);(20,21)(22,25)(23,26)(24,27)(28,32)(29,31)(30,33)(34,35);(20,22)(21,25)(23,28)(24,29)(26,32)(27,31)(30,34)(33,35);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,32,31,35)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13045, C₁₉×#13046, C₁₉×#21483, …
maximal normal subgroup of	C₁₉×#13045, C₁₉×#13046, C₁₉×#21483, …
maximal quotient of	C₁₉×#18122, C₁₉×#18123, C₁₉×#18124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1757);