C₂₉×#1614 #16815328

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1614

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂⁴×C₂₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

236 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 928

A minimal faithful permutation representation — 3 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)(31,34)(32,36)(35,37)(38,39,42,45)(40,46,48,53)(41,49,51,44)(43,50,52,47);(30,31,33,35)(32,37,36,34)(38,40,42,48)(39,43,45,52)(41,50,51,47)(44,53,49,46);(32,36)(34,37)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12214, C₂₉×#12216, C₂₉×#12218, …
maximal normal subgroup of	C₂₉×#12214, C₂₉×#12216, C₂₉×#12218, …
maximal quotient of	C₂₉×#7789, C₂₉×#7797, C₂₉×#7802, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 346);