C₂₉×#1916 #16815630

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#1916

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂²×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31)(32,33)(34,35)(36,39)(37,38)(40,41)(42,43,47,44,46,49,45,48);(35,38)(39,41)(42,44,47,49,46,48,45,43);(31,33)(34,36,37,40)(35,39,38,41)(42,45,46,47)(43,48,49,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1916, C₂₉×#21020, C₂₉×#21022, …
maximal normal subgroup of	C₂×C₂₉×#1916, C₂₉×#21020, C₂₉×#21022, …
maximal quotient of	C₂₉×#9533, C₂₉×#9534, C₂₉×#9535, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 648);

C29×#1916 #16815630