C₂₉×#2363 #16816077

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#2363

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(34,35,37,36)(38,39,42,41)(40,43,45,44);(34,36,37,35)(39,41)(43,44);(30,31)(32,33)(38,40,42,45)(39,43,41,44);(38,41,42,39)(40,44,45,43)

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#22857, C₂₉×#22860, C₂₉×#22865, …
maximal normal subgroup of	C₂₉×#22857, C₂₉×#22860, C₂₉×#22865, …
maximal quotient of	C₂₉×#13801, C₂₉×#13816, C₂₉×#13818, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1095);

C29×#2363 #16816077