C₂₉×#2984 #16816698

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

Aliases

direct product

C₂₉×#2984

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

364 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 272 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)(30,31,34,35,33,37,32,36)(38,39)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53);(30,32,33,34)(31,35,37,36)(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51);(30,32,33,34)(31,36,37,35)(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52);(31,37)(35,36)(39,45)(43,46)(44,53)(51,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9164, C₂₉×#9166, C₂₉×#9244, …
maximal normal subgroup of	C₂₉×#9164, C₂₉×#9166, C₂₉×#9244, …
maximal quotient of	C₂₉×#20535, C₂₉×#20572, C₂₉×#20573, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1716);