C₂₉×#2948 #16816662

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2948

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₈×C₂₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#117 ◁ G

528 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)(30,31,33,32)(34,35)(36,40)(37,39)(38,41)(42,45)(43,48)(44,46)(47,49);(35,39)(37,45)(40,46)(41,42)(44,49)(47,48);(30,32,33,31)(34,36)(35,40)(37,44)(38,43)(39,46)(41,48)(42,47)(45,49);(35,41)(36,43)(39,42)(44,49)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12826, C₂₉×#12940, C₂₉×#12953, …
maximal normal subgroup of	C₂₉×#12826, C₂₉×#12940, C₂₉×#12953, …
maximal quotient of	C₂₉×#17854, C₂₉×#17877, C₂₉×#17895, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1680);

C29×#2948 #16816662