C₂₉×#3428 #16817142

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

C₂₉×#3428

Subgroups

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

1540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 49 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#10743, C₂₉×#10747, C₂₉×#10752, …
maximal normal subgroup of	C₂₉×#10743, C₂₉×#10747, C₂₉×#10752, …
maximal quotient of	C₂₉×#33996, C₂₉×#33999, C₄×C₂₉×#518, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2160);

C29×#3428 #16817142