C₂₉×#1880 #16815594

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

Aliases

direct product

C₂₉×#1880

Subgroups

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

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 45 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)(38,39,42,45,43,40,41,44);(30,31,32,33)(38,40,43,39)(41,44,42,45);(35,37)(38,39,43,40)(41,45,42,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1880, C₂₉×#20924, C₂₉×#20926, …
maximal normal subgroup of	C₂×C₂₉×#1880, C₂₉×#20924, C₂₉×#20926, …
maximal quotient of	C₂₉×#8948, C₂₉×#8952, C₂₉×#8978, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 612);

C29×#1880 #16815594