C₂₉×#2551 #16816265

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2551

Subgroups

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

556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 3712

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)(38,39,42,45)(40,44,41,43);(30,31,33,32)(34,35,36,37)(38,40,42,41)(39,43,45,44);(34,35)(36,37)(38,40,42,41)(39,43,45,44);(30,32,33,31)(38,41,42,40)(39,44,45,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10348, C₂₉×#10349, C₂₉×#10350, …
maximal normal subgroup of	C₂₉×#10348, C₂₉×#10349, C₂₉×#10350, …
maximal quotient of	C₂₉×#13910, C₂₉×#14005, C₂₉×#14053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1283);