C₂₉×#2217 #16815931

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2217

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂₉×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

164 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 68 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)(35,39)(36,43)(37,44)(40,45)(41,49)(42,48)(46,47);(34,35,40,49,37,41,36,39,38,42,43,47,44,46,45,48);(31,33)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₉×#2217, C₂₉×#33600, C₂₉×#33605, …
maximal normal subgroup of	C₂×C₂₉×#2217, C₂₉×#33600, C₂₉×#33605, …
maximal quotient of	C₂₉×#12432, C₂₉×#12441, C₂₉×#12453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 949);