C₂₉×#2310 #16816024

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂₉×#2310

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

784 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 360 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) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 53 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)(31,33)(34,35,36,37)(39,43)(40,46)(41,49)(51,53);(38,39,42,43)(40,47,46,44)(41,45,49,50)(48,53,52,51);(30,31)(32,33)(34,35)(36,37)(38,40,42,46)(39,44,43,47)(41,48,49,52)(45,51,50,53);(38,41)(39,45)(40,48)(42,49)(43,50)(44,51)(46,52)(47,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8753, C₂₉×#8754, C₂₉×#9462, …
maximal normal subgroup of	C₂₉×#8753, C₂₉×#8754, C₂₉×#9462, …
maximal quotient of	C₂₉×#13776, C₂₉×#13786, C₂₉×#13795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1042);