C₁₉×#3416 #14561273

order	2432
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#3416

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₁₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ #41×C₁₉ ◁ C₁₉×#131 ◁ G

360 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 180 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,30)(22,27,31,41)(23,26,36,40)(24,37,35,29)(28,44,39,34)(32,38,45,49)(33,48,46,43)(42,51,50,47);(21,26)(23,34)(24,35)(27,38)(28,29)(30,40)(32,47)(33,46)(36,44)(37,39)(41,49)(42,43)(45,51)(48,50);(20,22)(21,27)(23,32)(24,33)(25,31)(26,38)(28,42)(29,43)(30,41)(34,47)(35,46)(36,45)(37,48)(39,50)(40,49)(44,51);(22,31)(27,41)(32,45)(33,46)(38,49)(42,50)(43,48)(47,51)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#33854, C₁₉×#33855, C₁₉×#33856, …
maximal normal subgroup of	C₁₉×#33854, C₁₉×#33855, C₁₉×#33856, …
maximal quotient of	C₁₉×#33381, C₁₉×#33382, C₁₉×#33411, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2148);