C₂₉×#1866 #16815580

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1866

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂²×C₂₉	C₄×D₄
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1866, C₂₉×#20884, C₂₉×#20885, …
maximal normal subgroup of	C₂×C₂₉×#1866, C₂₉×#20884, C₂₉×#20885, …
maximal quotient of	C₂₉×#8843, C₂₉×#8844, C₂₉×#8845, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 598);

C29×#1866 #16815580