C₂×C₂₉×#529 #16817153

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

Aliases

direct product

C₂×C₂₉×#529

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂³×C₂₉	C₂⁴
prime radical	C₂×C₂₉×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 generators on 47 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4)(5,8)(6,7)(9,10)(11,12)(13,15)(14,16)(17,18);(4,7)(8,10)(11,13,14,17)(12,15,16,18);(12,16)(15,18);(3,5,6,9)(4,8,7,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8315, C₂₉×#8330, C₂₉×#8336, …
maximal normal subgroup of	C₂₉×#8315, C₂₉×#8330, C₂₉×#8336, …
maximal quotient of	C₂×C₂₉×#2283, C₂×C₂₉×#2290, C₂×C₂₉×#2293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2171);

C2×C29×#529 #16817153