C₂₉×#2169 #16815883

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

Aliases

direct product

C₂₉×#2169

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₉	C₂³
commutator	C₂²	C₂²×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂²×C₂₉	C₂²×C₈
prime radical	C₂×D₄×C₂₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ G

162 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 1856

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)(30,31)(32,33)(34,35,38,42,39,36,43,45,37,40,46,48,47,44,41,49);(31,33)(35,40)(36,44)(42,48)(45,49);(34,36,38,45,39,40,43,48,37,44,46,49,47,35,41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7380, C₂₉×#12038, C₂₉×#12039, …
maximal normal subgroup of	C₂₉×#7380, C₂₉×#12038, C₂₉×#12039, …
maximal quotient of	C₂₉×#12039, C₂₉×#12051, C₂₉×#12054, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 901);