C₂₉×#1424 #16815138

order	3712
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#1424

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₉	D₁₆
commutator	C₁₆	C₂×C₄×C₂₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₉
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 2 generators on 65 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)(35,40)(36,45)(37,46)(38,49)(41,48)(42,57)(43,60)(44,54)(47,56)(50,63)(51,52)(53,58)(55,64)(59,65)(61,62);(34,35,41,55,37,42,47,53,49,58,62,57,63,64,36,40,39,44,45,52,50,59,61,60,38,43,56,65,46,51,48,54)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7540, C₂₉×#7548, C₂×C₂₉×#1424, …
maximal normal subgroup of	C₂₉×#7540, C₂₉×#7548, C₂×C₂₉×#1424, …
maximal quotient of	C₂₉×#7461, C₂₉×#7471, C₂₉×#7548, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 156);

C29×#1424 #16815138