C₂×C₂₉×#465 #16816761

order	3712
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₂₉×#465

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4)(5,6)(8,11)(9,13)(12,14);(7,8,9,11,10,12,13,14);(4,6)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9781, C₂₉×#9786, C₂₉×#9813, …
maximal normal subgroup of	C₂₉×#9781, C₂₉×#9786, C₂₉×#9813, …
maximal quotient of	C₂×C₂₉×#1665, C₂×C₂₉×#1671, C₂×C₂₉×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1779);

C2×C29×#465 #16816761