C₂₉×#3459 #16817173

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

Aliases

direct product

C₂₉×#3459

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

1160 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)(32,36)(33,35)(34,37)(38,39)(40,43)(41,42)(44,45);(30,32)(31,34)(33,37)(35,36);(32,37)(34,36)(39,42)(43,45);(31,35)(34,36);(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8317, C₂₉×#8399, C₂₉×#8401, …
maximal normal subgroup of	C₂₉×#8317, C₂₉×#8399, C₂₉×#8401, …
maximal quotient of	C₂₉×#34057, C₂₉×#34082, C₂₉×#34083, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2191);

C29×#3459 #16817173