C₂₉×#2003 #16815717

order	3712
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2003

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂×C₂₉×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

382 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 49
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2003, C₂₉×#23399, C₂₉×#23400, …
maximal normal subgroup of	C₂×C₂₉×#2003, C₂₉×#23399, C₂₉×#23400, …
maximal quotient of	C₂₉×#9915, C₂₉×#9921, C₂₉×#9923, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 735);