C₂₉×#1818 #16815532

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1818

Subgroups

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

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 57 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)(42,43,45,48,46,49,52,55)(44,47,51,54,50,53,56,57);(35,38)(39,41)(42,44)(43,47)(45,51)(46,50)(48,54)(49,53)(52,56)(55,57);(31,33)(34,36,37,40)(35,39,38,41)(44,50)(47,53)(51,56)(54,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7059, C₂₉×#7325, C₂₉×#7327, …
maximal normal subgroup of	C₂₉×#7059, C₂₉×#7325, C₂₉×#7327, …
maximal quotient of	C₂₉×#8702, C₂₉×#8703, C₂₉×#8704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 550);

C29×#1818 #16815532