C₂₉×#1303 #16815017

order	3712
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1303

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²⋊C₄
commutator	C₂×C₄	C₄²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂²×C₂₉
socle	C₂²×C₂₉	#95
prime radical	C₂³×C₂₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 928

A minimal faithful permutation representation — 2 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)(32,33)(36,37)(38,39,42,44,43,40,41,45);(30,31,33,36,34,37,32,35)(38,40,43,39)(41,44,42,45)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₉×#1303, C₂₉×#8092, C₂₉×#8093, …
maximal normal subgroup of	C₂×C₂₉×#1303, C₂₉×#8092, C₂₉×#8093, …
maximal quotient of	C₂₉×#7027, C₂₉×#7028, C₂₉×#7031, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 35);