C₁₉×#2825 #14560682

order	2432
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₁₉×#2825

Subgroups

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

522 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2825, C₁₉×#36670, C₁₉×#36676, …
maximal normal subgroup of	C₂×C₁₉×#2825, C₁₉×#36670, C₁₉×#36676, …
maximal quotient of	C₁₉×#14621, C₁₉×#14637, C₁₉×#14642, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1557);