C₁₉×#2145 #14560002

order	2432
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2145

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#102
commutator	C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₂×#102
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

224 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12646, C₁₉×#12649, C₁₉×#12741, …
maximal normal subgroup of	C₁₉×#12646, C₁₉×#12649, C₁₉×#12741, …
maximal quotient of	C₁₉×#11597, C₁₉×#11599, C₁₉×#11600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 877);