C₂₉×#2246 #16815960

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#2246

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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)(31,33)(35,39)(36,40)(37,43)(41,49)(42,47)(44,48)(45,46);(34,35,40,46,37,41,44,47,38,42,48,49,43,45,36,39);(30,31,32,33)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7444, C₂₉×#7448, C₂₉×#12316, …
maximal normal subgroup of	C₂₉×#7444, C₂₉×#7448, C₂₉×#12316, …
maximal quotient of	C₂₉×#12503, C₂₉×#12509, C₂₉×#12515, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 978);

C29×#2246 #16815960