C₂₉×#2613 #16816327

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂₉×#2613

Subgroups

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

1134 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 928

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

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#18224, C₂₉×#18226, C₂₉×#23903, …
maximal normal subgroup of	C₂₉×#18224, C₂₉×#18226, C₂₉×#23903, …
maximal quotient of	C₂₉×#14255, C₂₉×#14256, C₂₉×#14262, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1345);