C₂₉×#3444 #16817158

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3444

Subgroups

	subgroup	G/H
center	C₄²×C₂₉	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₂₉ ◁ G

1212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 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)(32,35)(33,34)(36,37)(38,39)(40,43)(41,42)(44,45);(31,34)(35,37);(39,42)(43,45);(38,40,41,44)(39,43,42,45);(30,32,33,36)(31,35,34,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12719, C₂₉×#17458, C₂₉×#17462, …
maximal normal subgroup of	C₂₉×#12719, C₂₉×#17458, C₂₉×#17462, …
maximal quotient of	C₂₉×#34012, C₂₉×#34026, C₄×C₂₉×#525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2176);

C29×#3444 #16817158