C₂₉×#2190 #16815904

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2190
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2190

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×M₁₆×C₂₉ ◁ G

226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 464

A minimal faithful permutation representation — 3 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)(31,35)(32,38)(33,41)(36,43)(37,44)(39,42)(40,45);(30,31)(32,39)(33,42)(34,36)(35,38)(37,41)(40,44)(43,45);(32,40)(35,43)(38,45)(39,44)

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12114, C₂₉×#12116, C₂₉×#12117, …
maximal normal subgroup of	C₂₉×#12114, C₂₉×#12116, C₂₉×#12117, …
maximal quotient of	C₂₉×#12102, C₂₉×#12103, C₂₉×#12104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 922);