C₁₉×#2120 #14559977

order	2432
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2120

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#99
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂³×C₁₉
socle	C₂×C₁₉	C₂×#99
prime radical	C₁₉×#525	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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 — 3 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)(22,26)(23,30,31,25)(24,27)(28,34,35,32)(29,33);(21,25)(26,32)(27,30)(33,34);(20,22,24,29)(21,26,27,33)(23,28,31,35)(25,32,30,34)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12623, C₁₉×#12624, C₁₉×#12711, …
maximal normal subgroup of	C₁₉×#12623, C₁₉×#12624, C₁₉×#12711, …
maximal quotient of	C₁₉×#11425, C₁₉×#11452, C₁₉×#11471, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 852);