C₂×C₂₉×#380 #16815992

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₂₉×#380

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂³
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

1232 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);(4,6)(7,8,9,10)(12,14);(11,12,13,14);(3,4)(5,6)(7,8)(9,10)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7915, C₂×C₂₉×#1289, C₂₉×#7983, …
maximal normal subgroup of	C₂₉×#7915, C₂×C₂₉×#1289, C₂₉×#7983, …
maximal quotient of	C₂×C₂₉×C₂²⋊#95, C₂×C₂₉×#1434, C₂×C₂₉×C₄⋊#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1010);

C2×C29×#380 #16815992