C₂₉×#2369 #16816083

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

Aliases

direct product

C₂₉×#2369

Subgroups

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

496 conjugacy classes of subgroups; only the 328 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 328 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) = 3712

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)(30,31,33,32)(34,35,38,37)(36,40,41,39)(43,46)(47,48);(30,32,33,31)(35,37)(39,40)(42,43)(44,48)(45,46)(47,49);(34,36,38,41)(35,39,37,40);(34,37,38,35)(36,40,41,39)(42,44,45,49)(43,47,46,48)

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8927, C₂₉×#8928, C₂₉×#8929, …
maximal normal subgroup of	C₂₉×#8927, C₂₉×#8928, C₂₉×#8929, …
maximal quotient of	C₄⋊C₄²×C₂₉, C₂₉×#13818, C₂₉×#13826, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1101);