C₂×C₂₉×#446 #16816673

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₂₉×#446

Subgroups

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

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 3712

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)(5,10)(6,8)(7,9)(11,12,14,13,15,16,18,17);(3,5,7,6)(4,8,9,10);(3,6,7,5)(4,8,9,10)(11,13,14,16,15,17,18,12)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8167, C₂₉×#8207, C₂₉×#8209, …
maximal normal subgroup of	C₂₉×#8167, C₂₉×#8207, C₂₉×#8209, …
maximal quotient of	C₂×C₂₉×#1771, C₂×C₂₉×#1770, C₄×C₂₉×#446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1691);

C2×C29×#446 #16816673