C₂₉×#2112 #16815826

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2112

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	C₂⁴×C₂₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ G

260 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 128 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) = 928

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7184, C₂₉×#7185, C₂₉×#7200, …
maximal normal subgroup of	C₂₉×#7184, C₂₉×#7185, C₂₉×#7200, …
maximal quotient of	C₂₉×#11418, C₂₉×#11440, C₂₉×#11460, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 844);