C₂×C₂₉×#568 #16817286

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₂₉×#568

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₄	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂²×#41×C₂₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 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);(3,4,6,10,7,9,13,16)(5,8,12,15,11,14,17,18);(3,5)(4,8)(6,12)(7,11)(9,14)(10,15)(13,17)(16,18);(5,11)(8,14)(12,17)(15,18);(4,9)(8,14)(10,16)(15,18)

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#10742, C₂₉×#10744, C₂₉×#10746, …
maximal normal subgroup of	C₂₉×#10742, C₂₉×#10744, C₂₉×#10746, …
maximal quotient of	C₂×C₂₉×#2873, C₂×C₂₉×#2875, C₄×C₂₉×#568, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2304);

C2×C29×#568 #16817286