C₂₉×#2163 #16815877

order	3712
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2163

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	C₂³×C₂₉	C₂×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ G

152 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 104 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) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 53 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)(32,35)(33,34)(36,37)(38,39,40,44,41,45,46,51,42,43,47,49,48,50,52,53);(31,34)(35,37);(30,32,33,36)(31,35,34,37)(39,43)(44,49)(45,50)(51,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7143, C₂₉×#7144, C₂₉×#7146, …
maximal normal subgroup of	C₂₉×#7143, C₂₉×#7144, C₂₉×#7146, …
maximal quotient of	C₂₉×#12591, C₂₉×#12599, C₂₉×#12653, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 895);