C₂₉×#2875 #16816589

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#2875

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂	C₂²×C₄²×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

556 conjugacy classes of subgroups; only the 504 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 504 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) = 1856

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

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9311, C₂₉×#9312, C₂₉×#12609, …
maximal normal subgroup of	C₂₉×#9311, C₂₉×#9312, C₂₉×#12609, …
maximal quotient of	C₂₉×#17316, C₂₉×#17320, C₂₉×#17329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1607);