C₂×C₂₉×#428 #16816624

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₂₉×#428

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10896, C₂₉×#10899, C₂₉×#10903, …
maximal normal subgroup of	C₂₉×#10896, C₂₉×#10899, C₂₉×#10903, …
maximal quotient of	C₂×C₂₉×#1565, C₂×C₂₉×#1569, C₂₉×#17796, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1642);

C2×C29×#428 #16816624