C₂₉×#3549 #16817263

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

C₂₉×#3549

Subgroups

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

1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 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 — 5 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)(31,33)(35,36)(39,42)(40,41);(30,31,34,33)(32,36,37,35)(38,39,43,42)(40,45,41,44);(38,40,43,41)(39,44,42,45);(30,32,34,37)(31,35,33,36)(38,41,43,40)(39,45,42,44);(30,33,34,31)(32,36,37,35)(38,42,43,39)(40,45,41,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8491, C₂₉×#8530, C₂₉×#12769, …
maximal normal subgroup of	C₂₉×#8491, C₂₉×#8530, C₂₉×#12769, …
maximal quotient of	C₂₉×#34368, C₂₉×#34415, C₂₉×#34485, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2281);