C₂₉×#1923 #16815637

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#1923

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂²×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂³×C₂₉	C₂²×C₄
prime radical	C₂⁴×C₂₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 45 points:

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

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₉×#1923, C₂₉×#21046, C₂₉×#21048, …
maximal normal subgroup of	C₂×C₂₉×#1923, C₂₉×#21046, C₂₉×#21048, …
maximal quotient of	C₂₉×#9541, C₂₉×#9542, C₂₉×#9543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 655);

C29×#1923 #16815637