C₁₉×#2237 #14560094

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#2237

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,33,38)(30,34,41,49)(31,35,44,51)(32,45,43,37)(36,52,50,42)(39,46,55,58)(40,56,54,48)(47,59,57,53);(21,24)(25,27)(28,30,33,41)(29,34,38,49)(31,39,44,55)(32,40,43,54)(35,46,51,58)(36,47,50,57)(37,48,45,56)(42,53,52,59);(20,22,23,26)(21,25,24,27)(29,35)(31,42)(32,43)(34,46)(36,37)(38,51)(39,53)(40,54)(44,52)(45,50)(47,48)(49,58)(55,59)(56,57)

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2237, C₁₉×#33645, C₁₉×#33647, …
maximal normal subgroup of	C₂×C₁₉×#2237, C₁₉×#33645, C₁₉×#33647, …
maximal quotient of	C₁₉×#12868, C₁₉×#12921, C₁₉×#12994, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 969);