C₂₉×#1271 #16814985

order	3712
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#1271

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₈×C₂₉
Frattini, cosocle	C₂×C₄²	C₂²×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

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

normal subgroups only

This group has 158 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) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 2 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)(32,36,37,34)(33,35)(39,42,43,44)(46,47,48,50,49,51,52,53);(30,32,33,37)(31,34,35,36)(38,39)(40,44)(41,43)(42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#1271, C₂₉×#7560, C₂₉×#7562, …
maximal normal subgroup of	C₂×C₂₉×#1271, C₂₉×#7560, C₂₉×#7562, …
maximal quotient of	C₂₉×#7025, C₂₉×#7118, C₂₉×#7119, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 3);