C₂×C₂₉×#330 #16815237

order	3712
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂×C₂₉×#330

Subgroups

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

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₂₉×#330, C₂₉×#8225, C₂₉×#8227, …
maximal normal subgroup of	C₄×C₂₉×#330, C₂₉×#8225, C₂₉×#8227, …
maximal quotient of	C₂×C₂₉×#1271, C₂₉×#7568, C₂₉×#7627, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 255);

C2×C29×#330 #16815237