C₁₉×H(7,𝔽₂) #14561451

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(7,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₉ · Schur multiplier (H₂) = C₂¹⁴

Aliases

direct product

C₁₉×H(7,𝔽₂)

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ G

5992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 6 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)(24,25)(27,31)(28,32)(29,35)(33,34);(21,25)(26,32)(27,30)(33,35);(22,28)(26,32)(29,34)(33,35);(20,22)(21,26)(23,29)(24,28)(25,32)(27,33)(30,35)(31,34);(20,21)(22,26)(23,27)(24,25)(28,32)(29,33)(30,31)(34,35);(20,23)(21,27)(22,29)(24,31)(25,30)(26,33)(28,34)(32,35)

Conjugacy classes & character table

1235 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#32894, C₁₉×#32896, C₁₉×#60388, …
maximal normal subgroup of	C₁₉×#32894, C₁₉×#32896, C₁₉×#60388, …
maximal quotient of	C₁₉×#62652, C₁₉×#62654, C₁₉×#62842, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2326);

C19×H(7,𝔽2) #14561451