C₄×C₁₉×#135 #14560796

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄×C₁₉×#135

Subgroups

	subgroup	G/H
center	C₄²×C₁₉	D₄
commutator	C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×C₁₉×#135	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(5,6)(7,14)(8,12)(9,17)(10,13)(11,15)(16,19)(18,20);(5,7)(6,11)(8,15)(9,18)(10,16)(12,19)(13,20)(14,17);(5,8,10,9)(6,12,13,17)(7,15,16,18)(11,19,20,14)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#11591, C₁₉×#11592, C₁₉×#11597, …
maximal normal subgroup of	C₁₉×#11591, C₁₉×#11592, C₁₉×#11597, …
maximal quotient of	C₈×C₁₉×#135, C₁₉×#17863, C₁₉×#17886, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1671);

C4×C19×#135 #14560796