C₂₉×#1835 #16815549

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

Aliases

direct product

C₂₉×#1835

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

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 3712

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)(44,52)(45,48)(46,56)(47,51)(49,54)(50,53)(55,57);(35,38)(39,41)(42,44,53,55,47,54,46,45)(43,48,56,49,51,57,50,52);(34,36,37,40)(35,39,38,41)(42,45,46,54,47,55,53,44)(43,49,50,48,51,52,56,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7218, C₂₉×#7221, C₂₉×#7366, …
maximal normal subgroup of	C₂₉×#7218, C₂₉×#7221, C₂₉×#7366, …
maximal quotient of	C₂₉×#8785, C₂₉×#8788, C₂₉×#8791, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 567);

C29×#1835 #16815549