C₁₉×#2238 #14560095

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2238
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2238

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#481
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₁₉×#469	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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)(21,25)(22,28)(23,31)(26,33)(27,30)(29,35)(32,34);(22,29)(25,33)(28,35)(30,34);(20,21,23,32,24,26,31,27)(22,30,28,33,29,34,35,25)

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12298, C₁₉×#12300, C₁₉×#12301, …
maximal normal subgroup of	C₁₉×#12298, C₁₉×#12300, C₁₉×#12301, …
maximal quotient of	C₁₉×#12875, C₁₉×#12931, C₁₉×#13010, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 970);