C₂×C₁₉×#470 #14560910

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₁₉×#470

Subgroups

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

492 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 41 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1340, C₂×C₁₉×#1342, C₁₉×#13000, …
maximal normal subgroup of	C₂×C₁₉×#1340, C₂×C₁₉×#1342, C₁₉×#13000, …
maximal quotient of	C₂×C₁₉×#1689, C₂×C₁₉×#1695, C₂×C₁₉×#1703, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1785);