C₁₉×#2875 #14560732

order	2432
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₉×#2875

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator	C₂	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

556 conjugacy classes of subgroups; only the 504 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 504 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) = 39
transitive degree	μ_t(G) = 1216

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

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

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#9311, C₁₉×#9312, C₁₉×#12609, …
maximal normal subgroup of	C₁₉×#9311, C₁₉×#9312, C₁₉×#12609, …
maximal quotient of	C₁₉×#17316, C₁₉×#17320, C₁₉×#17329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1607);