C₂₉×#1415 #16815129

order	3712
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1415

Subgroups

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

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1415, C₂₉×#13615, C₂₉×#13616, …
maximal normal subgroup of	C₂×C₂₉×#1415, C₂₉×#13615, C₂₉×#13616, …
maximal quotient of	C₂₉×#7383, C₂₉×#7418, C₂₉×#7444, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 147);

C29×#1415 #16815129