C₂₉×#2381 #16816095

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2381

Subgroups

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

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(35,38)(36,40)(43,47)(44,50)(49,52)(51,56);(35,38)(39,41)(42,43,46,47)(44,48,50,54)(45,52,53,49)(51,57,56,55);(34,35,37,38)(36,39,40,41)(42,44)(43,48)(45,51)(46,50)(47,54)(49,55)(52,57)(53,56);(34,36)(35,39)(37,40)(38,41)(42,45,46,53)(43,49,47,52)(44,51,50,56)(48,55,54,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9426, C₂₉×#9427, C₂₉×#9429, …
maximal normal subgroup of	C₂₉×#9426, C₂₉×#9427, C₂₉×#9429, …
maximal quotient of	C₂₉×#13830, C₂₉×#13833, C₂₉×#13834, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1113);

C29×#2381 #16816095