C₂×C₂₉×#340 #16815448

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₂₉×#340

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₉	D₄
commutator	C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

512 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);(3,4)(5,6)(7,8,9,10)(12,16)(13,14)(17,18);(4,6)(11,12,14,17,15,18,13,16)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7258, C₂₉×#7264, C₄×C₂₉×#340, …
maximal normal subgroup of	C₂₉×#7258, C₂₉×#7264, C₄×C₂₉×#340, …
maximal quotient of	C₂×C₂₉×#1277, C₂₉×#7874, C₂₉×#7877, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 466);

C2×C29×#340 #16815448