C₂₉×#2483 #16816197

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

Aliases

direct product

C₂₉×#2483

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

700 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 49
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9500, C₂₉×#9502, C₂₉×#10338, …
maximal normal subgroup of	C₂₉×#9500, C₂₉×#9502, C₂₉×#10338, …
maximal quotient of	C₂₉×#13869, C₂₉×#13992, C₂₉×#14040, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1215);