C₂₉×#2978 #16816692

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

Aliases

direct product

C₂₉×#2978

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂₉×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 53 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)(32,36)(33,35)(34,37)(38,39,41,45,42,44,48,51)(40,43,47,50,46,49,52,53);(30,32)(31,34)(33,37)(35,36)(38,40)(39,43)(41,47)(42,46)(44,49)(45,50)(48,52)(51,53);(32,37)(34,36)(39,44)(40,46)(45,51)(47,52);(31,35)(34,36)(40,46)(43,49)(47,52)(50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9331, C₂₉×#9332, C₂₉×#12963, …
maximal normal subgroup of	C₂₉×#9331, C₂₉×#9332, C₂₉×#12963, …
maximal quotient of	C₂₉×#20529, C₂₉×#20532, C₂₉×#20542, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1710);

C29×#2978 #16816692