C₂₉×#2921 #16816635

order	3712
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2921

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂⁴×C₂₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

392 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 928

A minimal faithful permutation representation — 4 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)(38,39,41,45,42,44,48,51)(40,43,47,50,46,49,52,53);(31,34)(35,37)(38,40)(39,43)(41,47)(42,46)(44,49)(45,50)(48,52)(51,53);(30,32,33,36)(31,35,34,37)(40,46)(43,49)(47,52)(50,53);(39,44)(43,49)(45,51)(50,53)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8863, C₂₉×#9034, C₂₉×#9036, …
maximal normal subgroup of	C₂₉×#8863, C₂₉×#9034, C₂₉×#9036, …
maximal quotient of	C₂₉×#20365, C₂₉×#20377, C₂₉×#20429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1653);