C₂₉×#2901 #16816615

order	3712
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#2901

Subgroups

	subgroup	G/H
center	C₄×C₂₉	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂×C₂₉	C₂²×C₂²⋊C₄
prime radical	C₂₉×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

738 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 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)(30,31,34,38,35,32,39,37)(33,36,42,44,41,40,45,43);(30,32)(31,35)(33,40)(34,37)(36,41)(38,39)(42,43)(44,45);(30,33)(31,36)(32,40)(34,42)(35,41)(37,43)(38,44)(39,45);(33,41)(36,40)(42,45)(43,44)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#22461, C₂₉×#22462, C₂₉×#22898, …
maximal normal subgroup of	C₂₉×#22461, C₂₉×#22462, C₂₉×#22898, …
maximal quotient of	C₂₉×#17438, C₂₉×#17439, C₂₉×#17453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1633);