C₂×C₂₉×#344 #16815457

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₂₉×#344

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²⋊C₄
commutator	C₂²	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂²×C₂₉	#95
prime radical	C₂⁴×C₂₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×C₂₉×#344, C₂₉×#10711, C₂₉×#10729, …
maximal normal subgroup of	C₄×C₂₉×#344, C₂₉×#10711, C₂₉×#10729, …
maximal quotient of	C₂×C₂₉×#1281, C₂₉×#7918, C₂₉×#7919, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 475);

C2×C29×#344 #16815457