C₁₉×#3573 #14561430

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₁₉×#3573

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂⁴
commutator	C₂	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₄	C₂⁵×C₁₉
socle	C₂×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#585	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ G

1424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 5 generators on 51 points:

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

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#12684, C₁₉×#12685, C₁₉×#21477, …
maximal normal subgroup of	C₁₉×#12684, C₁₉×#12685, C₁₉×#21477, …
maximal quotient of	C₁₉×#60058, C₁₉×#60065, C₁₉×#60100, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2305);

C19×#3573 #14561430