C₂₉×#3058 #16816772

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#3058

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

524 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 928

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

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#11868, C₂₉×#11870, C₂₉×#13074, …
maximal normal subgroup of	C₂₉×#11868, C₂₉×#11870, C₂₉×#13074, …
maximal quotient of	C₂₉×#19187, C₂₉×#19192, C₂₉×#19198, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1790);