C₂×C₂₉×#397 #16816104

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₂₉×#397

Subgroups

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

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9025, C₂₉×#9028, C₂₉×#9918, …
maximal normal subgroup of	C₂₉×#9025, C₂₉×#9028, C₂₉×#9918, …
maximal quotient of	C₂×C₂₉×#1439, C₂×C₂₉×#1440, C₂×C₂₉×#1442, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1122);

C2×C29×#397 #16816104