C₂₉×#2983 #16816697

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

Aliases

direct product

C₂₉×#2983

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	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

356 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

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)(30,31,32,35,33,34,36,37)(38,39)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51);(31,34)(35,37)(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52);(39,45)(43,46)(44,53)(51,52)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8838, C₂₉×#8865, C₂₉×#8962, …
maximal normal subgroup of	C₂₉×#8838, C₂₉×#8865, C₂₉×#8962, …
maximal quotient of	C₂₉×#20534, C₂₉×#20536, C₂₉×#20570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1715);