C₂×C₁₉×#585 #14561450

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₉ · Schur multiplier (H₂) = C₂¹⁴

Aliases

direct product

C₂×C₁₉×#585

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₉
socle	C₂²×C₁₉	C₂⁵
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

5956 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 6 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4)(5,11)(6,10)(7,9)(8,12)(13,17)(14,16)(15,18);(3,5)(4,8)(6,13)(7,12)(9,11)(10,15)(14,18)(16,17);(5,12)(8,11)(13,18)(15,17);(4,9)(8,11)(10,16)(15,17);(3,6,7,14)(4,10,9,16)(5,13,12,18)(8,15,11,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₉×#20606, C₁₉×#20608, C₁₉×#20610, …
maximal normal subgroup of	C₁₉×#20606, C₁₉×#20608, C₁₉×#20610, …
maximal quotient of	C₂×C₁₉×#3428, C₂×C₄×C₁₉×H(5,𝔽₂), C₂×C₄×C₁₉×2₋¹⁺⁴, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2325);

C2×C19×#585 #14561450