C₂₉×#2356 #16816070

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

Aliases

direct product

C₂₉×#2356

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

464 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)(34,35,38,37)(36,39,41,40)(44,48)(46,49);(35,37)(39,40)(42,43,45,47)(44,46,48,49);(34,36,38,41)(35,39,37,40)(42,44,45,48)(43,46,47,49);(34,37,38,35)(36,40,41,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8768, C₂₉×#8769, C₂₉×#8774, …
maximal normal subgroup of	C₂₉×#8768, C₂₉×#8769, C₂₉×#8774, …
maximal quotient of	C₂₉×#13804, C₂₉×#13806, C₂₉×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1088);

C29×#2356 #16816070