C₂×C₂₉×#575 #16817294

order	3712
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₂₉×#575

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂²×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

1484 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)(5,12)(6,11)(7,15)(8,10)(9,13)(14,18)(16,17);(3,5)(4,9)(6,13)(7,16)(8,14)(10,17)(11,18)(12,15);(4,10)(9,17)(11,15)(12,18);(3,6,8,7)(4,11,10,15)(5,13,14,16)(9,18,17,12)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#11018, C₂₉×#11019, C₂₉×#11032, …
maximal normal subgroup of	C₂₉×#11018, C₂₉×#11019, C₂₉×#11032, …
maximal quotient of	C₂×C₂₉×#2896, C₂×C₂₉×#2911, C₂×C₂₉×#2943, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2312);

C2×C29×#575 #16817294