C₂×Q₈²×C₁₉ #14561334

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×Q₈²×C₁₉

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 5 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);(3,4,5,6)(7,10,9,8);(3,7,5,9)(4,8,6,10);(11,12,13,14)(15,18,17,16);(11,15,13,17)(12,16,14,18)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8396, C₁₉×#8451, C₁₉×#12777, …
maximal normal subgroup of	C₁₉×#8396, C₁₉×#8451, C₁₉×#12777, …
maximal quotient of	C₂×Q₈×C₄⋊C₄×C₁₉, C₂×C₁₉×#2369, C₄×Q₈²×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2209);

C2×Q82×C19 #14561334

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×Q₈²×C₁₉ #14561334