C₂₉×#1831 #16815545

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#1831

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂²×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle, prime radical	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

260 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 160 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) = 3712

A minimal faithful permutation representation — 3 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)(31,32)(34,35)(36,39)(37,38)(40,41)(42,43,44,46,45,47,48,49);(30,31,33,32)(35,38)(39,41);(30,32,33,31)(34,36,37,40)(35,39,38,41)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7018, C₂₉×#7022, C₂₉×#7030, …
maximal normal subgroup of	C₂₉×#7018, C₂₉×#7022, C₂₉×#7030, …
maximal quotient of	C₂₉×#8780, C₂₉×#8781, C₂₉×#8784, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 563);