C₂₉×#2858 #16816572

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₂₉×#2858

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

752 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 264 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 — 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)(31,32)(35,36)(40,43)(41,45);(30,31,33,32)(34,35,37,36)(38,39,42,44)(40,41,43,45);(34,35,37,36)(38,40,42,43)(39,41,44,45);(30,32,33,31)(34,36,37,35)(38,41)(39,43)(40,44)(42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7659, C₂₉×#7679, C₂₉×#7699, …
maximal normal subgroup of	C₂₉×#7659, C₂₉×#7679, C₂₉×#7699, …
maximal quotient of	C₂₉×#14687, C₂₉×#14700, C₂₉×#14708, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1590);