C₂×C₂₉×#432 #16816632

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

Aliases

direct product

C₂×C₂₉×#432

Subgroups

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

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(11,12,13,16,14,15,17,18);(4,7)(8,10);(3,5,6,9)(4,8,7,10)(12,15)(16,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7863, C₂₉×#7864, C₂₉×#7875, …
maximal normal subgroup of	C₂₉×#7863, C₂₉×#7864, C₂₉×#7875, …
maximal quotient of	C₂×C₂₉×#1745, C₂×C₂₉×#1749, C₂×C₂₉×#1767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1650);

C2×C29×#432 #16816632