C₂₉×#2344 #16816058

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#2344

Subgroups

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

604 conjugacy classes of subgroups.

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)(30,31,33,32)(34,35,36,37)(40,44)(42,45);(31,32)(38,39,41,43)(40,42,44,45);(38,40)(39,42)(41,44)(43,45);(30,32,33,31)

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9256, C₂₉×#9260, C₂₉×#22406, …
maximal normal subgroup of	C₂₉×#9256, C₂₉×#9260, C₂₉×#22406, …
maximal quotient of	C₂₉×#13799, C₂²⋊C₄×C₄⋊C₄×C₂₉, C₂₉×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1076);

C29×#2344 #16816058