C₂₉×#2320 #16816034

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

Aliases

direct product

C₂₉×#2320

Subgroups

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

444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 49 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)(35,38)(39,41)(43,45)(44,48);(42,43,46,45)(44,49,48,47);(34,35)(36,39)(37,38)(40,41)(42,44,46,48)(43,47,45,49);(34,36,37,40)(35,39,38,41)(42,45,46,43)(44,49,48,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9328, C₂₉×#9330, C₂₉×#17601, …
maximal normal subgroup of	C₂₉×#9328, C₂₉×#9330, C₂₉×#17601, …
maximal quotient of	C₂₉×#13781, C₂₉×#13783, C₂₉×#13786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1052);

C29×#2320 #16816034