C₂×C₂₉×#413 #16816601

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₂₉×#413

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₂₉	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10744, C₂₉×#10746, C₂₉×#10747, …
maximal normal subgroup of	C₂₉×#10744, C₂₉×#10746, C₂₉×#10747, …
maximal quotient of	C₂×C₂₉×#1458, C₂×C₂₉×#1459, C₂₉×#17349, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1619);

C2×C29×#413 #16816601