C₂₉×#3483 #16817197

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3483

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 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) = 1856

A minimal faithful permutation representation — 5 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)(31,35)(36,37)(38,39)(40,43)(41,45)(42,44);(30,31,34,35)(32,36,33,37)(38,40,43,39)(41,45,42,44);(30,32,34,33)(31,36,35,37)(38,41,43,42)(39,44,40,45);(30,32,34,33)(31,37,35,36)(38,42,43,41)(39,44,40,45);(30,33,34,32)(31,37,35,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8441, C₂₉×#12773, C₂₉×#17520, …
maximal normal subgroup of	C₂₉×#8441, C₂₉×#12773, C₂₉×#17520, …
maximal quotient of	C₂₉×#34129, C₂₉×#34155, C₄×C₂₉×#550, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2215);