C₂₉×#1603 #16815317

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

Aliases

direct product

C₂₉×#1603

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

244 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 64 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)(34,37)(38,39,43,46)(40,47,49,52)(41,45,42,50)(44,51,53,48);(30,31)(32,34)(33,35)(36,37)(38,40)(39,44)(41,48)(42,51)(43,49)(45,52)(46,53)(47,50);(30,32)(31,34)(33,36)(35,37)(38,41,43,42)(39,45,46,50)(40,48,49,51)(44,52,53,47)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#1603, C₂₉×#18100, C₂₉×#18127, …
maximal normal subgroup of	C₂×C₂₉×#1603, C₂₉×#18100, C₂₉×#18127, …
maximal quotient of	C₂₉×#7751, C₂₉×#7753, C₂₉×#7756, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 335);