C₂×C₂₉×#401 #16816114

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₂₉×#401

Subgroups

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

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 4 generators on 55 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(5,9)(7,10)(12,15)(16,17)(19,20,22,24)(21,25,26,23);(3,4,6,8)(5,10,9,7)(11,12,14,15)(13,17,18,16)(19,20)(21,25)(22,24)(23,26);(3,5)(4,7)(6,9)(8,10)(11,13,14,18)(12,16,15,17)(19,21,22,26)(20,23,24,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×C₂₉×#401, C₂₉×#14251, C₂₉×#14333, …
maximal normal subgroup of	C₄×C₂₉×#401, C₂₉×#14251, C₂₉×#14333, …
maximal quotient of	C₂×C₂₉×#1443, C₄×C₂₉×#401, C₂₉×C₂²⋊#401, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1132);

C2×C29×#401 #16816114