C₁₉×#2975 #14560832

order	2432
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2975

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂²×D₄×C₁₉	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

452 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 268 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) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8837, C₁₉×#8860, C₁₉×#8961, …
maximal normal subgroup of	C₁₉×#8837, C₁₉×#8860, C₁₉×#8961, …
maximal quotient of	C₁₉×#20524, C₁₉×#20536, C₁₉×#20568, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1707);