C₂₉×#2396 #16816110

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2396

Subgroups

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

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(34,35)(36,39)(37,38)(40,41)(42,43,45,47)(44,48,49,46);(30,31)(32,33)(35,38)(39,41);(31,33)(42,44,45,49)(43,46,47,48);(34,36,37,40)(35,39,38,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9033, C₂₉×#9034, C₂₉×#11715, …
maximal normal subgroup of	C₂₉×#9033, C₂₉×#9034, C₂₉×#11715, …
maximal quotient of	C₂₉×#13844, C₂₉×#13846, C₂₉×#13848, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1128);

C29×#2396 #16816110