C₂₉×#3093 #16816807

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#3093

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 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)(40,43)(41,44)(42,45)(46,49)(47,50)(48,51)(52,53);(31,34)(35,37)(38,40,42,48)(39,43,45,51)(41,47,49,53)(44,50,46,52);(30,32,33,36)(31,35,34,37)(39,44)(41,49)(43,50)(45,46)(47,53)(51,52);(39,45)(43,51)(44,46)(50,52)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#24020, C₂₉×#24021, C₂₉×#24022, …
maximal normal subgroup of	C₂₉×#24020, C₂₉×#24021, C₂₉×#24022, …
maximal quotient of	C₂₉×#20701, C₂₉×#20845, C₂₉×#20910, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1825);