C₂₉×#2241 #16815955

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

Aliases

direct product

C₂₉×#2241

Subgroups

	subgroup	G/H
center, socle, prime radical	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

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 53 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)(32,35)(33,34)(36,37)(38,39,45,40)(41,42,51,53)(43,50,46,47)(44,52,49,48);(31,34)(35,37)(38,40,43,51,44,52,42,50,45,39,46,41,49,48,53,47);(30,32,33,36)(31,35,34,37)(38,41,42,40,49,50,43,48,45,51,53,39,44,47,46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12344, C₂₉×#12345, C₂₉×#12346, …
maximal normal subgroup of	C₂₉×#12344, C₂₉×#12345, C₂₉×#12346, …
maximal quotient of	C₂₉×#12888, C₂₉×#13148, C₂₉×#13203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 973);

C29×#2241 #16815955