C₂₉×#2328 #16816042

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂₉×#2328

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

740 conjugacy classes of subgroups; only the 296 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 296 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) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(31,33)(34,35,37,36)(38,39,42,40)(41,44,45,43);(34,36,37,35)(39,40)(43,44);(30,31,32,33)(38,40,42,39)(41,44,45,43);(38,41,42,45)(39,43,40,44)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9101, C₂₉×#9105, C₂₉×#9295, …
maximal normal subgroup of	C₂₉×#9101, C₂₉×#9105, C₂₉×#9295, …
maximal quotient of	C₂₉×#13779, C₂₉×#13785, C₂₉×#13791, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1060);