C₂₉×#2929 #16816643

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

Aliases

direct product

C₂₉×#2929

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₉	C₂³
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂₉×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ G

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

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)(34,35,37,41,38,40,44,47)(36,39,42,46,43,45,48,49);(31,33);(34,36,37,42,38,43,44,48)(35,39,41,46,40,45,47,49);(35,40)(39,45)(41,47)(46,49)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8238, C₂₉×#8239, C₂₉×#8240, …
maximal normal subgroup of	C₂₉×#8238, C₂₉×#8239, C₂₉×#8240, …
maximal quotient of	C₂₉×#17900, C₂₉×#17901, C₂₉×#17902, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1661);

C29×#2929 #16816643