C₂₉×#1828 #16815542

order	3712
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1828

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#381
commutator	C₂³	C₂²×C₄×C₂₉
Frattini, cosocle	C₂⁴	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂⁴×C₂₉ ◁ G

296 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 45
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 3 generators on 45 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)(32,38,40,35)(33,41)(34,37)(36,42)(39,43,45,44);(30,32)(31,35)(33,39)(34,40)(36,43)(37,38)(41,44)(42,45);(30,33)(31,36,37,41)(32,39)(34,42)(35,43,38,44)(40,45)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12725, C₂₉×#12726, C₂₉×#12727, …
maximal normal subgroup of	C₂₉×#12725, C₂₉×#12726, C₂₉×#12727, …
maximal quotient of	C₂₉×#8734, C₂₉×#8735, C₂₉×#8736, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 560);