C₂₉×#2162 #16815876

order	3712
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#2162

Subgroups

	subgroup	G/H
center	C₄×C₈×C₂₉	C₂²
commutator	C₂	C₂²×C₁₆×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂²×C₂₉	C₂²×C₈
prime radical	C₂³×C₂₉	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₉ ◁ G

160 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 53 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)(32,35)(33,34)(36,37)(38,39,40,43,41,44,46,49,42,45,47,50,48,51,52,53);(31,34)(35,37);(30,32,33,36)(31,35,34,37)

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7142, C₂₉×#7144, C₂₉×#7145, …
maximal normal subgroup of	C₂₉×#7142, C₂₉×#7144, C₂₉×#7145, …
maximal quotient of	C₂₉×#12590, C₄×C₂₉×C₂²⋊C₁₆, C₄×C₂₉×C₄⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 894);