C₂×C₂₉×#383 #16815996

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₂₉×#383

Subgroups

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

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4,5,6)(9,13)(11,14)(16,19)(17,21);(7,8,10,12)(9,11,13,14)(15,16)(17,20)(18,19)(21,22);(7,9)(8,11)(10,13)(12,14)(15,17,18,21)(16,20,19,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7916, C₂×C₂₉×#1288, C₂₉×#7975, …
maximal normal subgroup of	C₂₉×#7916, C₂×C₂₉×#1288, C₂₉×#7975, …
maximal quotient of	C₂×C₂₉×#1434, C₄×C₂₉×#383, C₂×C₂₉×#1443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1014);

C2×C29×#383 #16815996