C₁₉×#1790 #14559647

order	2432
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#1790

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#120
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂³×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

670 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 31
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#13041, C₁₉×#13042, C₁₉×#13043, …
maximal normal subgroup of	C₁₉×#13041, C₁₉×#13042, C₁₉×#13043, …
maximal quotient of	C₁₉×#8316, C₁₉×#8317, C₁₉×#8346, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 522);