C₂₉×#2283 #16815997

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

Aliases

direct product

C₂₉×#2283

Subgroups

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

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(36,39)(37,38)(40,41)(42,43)(44,46)(45,47)(48,49);(35,38)(39,41)(42,44,45,48)(43,46,47,49);(43,47)(46,49);(34,36,37,40)(35,39,38,41)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7857, C₂₉×#7858, C₂₉×#7894, …
maximal normal subgroup of	C₂₉×#7857, C₂₉×#7858, C₂₉×#7894, …
maximal quotient of	C₂₉×#13753, C₂₉×#13755, C₂₉×#13757, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1015);

C29×#2283 #16815997