C₂₉×#1878 #16815592

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#1878

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

338 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)(31,33)(34,35)(36,37)(38,39,42,44,43,47,41,46)(40,48,50,45,51,52,49,53);(30,31,32,33)(39,44)(41,42)(45,48)(46,47)(49,50)(52,53);(35,37)(38,40,43,51)(39,45,47,53)(41,50,42,49)(44,48,46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1878, C₂₉×#20924, C₂₉×#20926, …
maximal normal subgroup of	C₂×C₂₉×#1878, C₂₉×#20924, C₂₉×#20926, …
maximal quotient of	C₂₉×#8946, C₂₉×#8950, C₂₉×#8974, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 610);

C29×#1878 #16815592