C₂×C₂₉×#485 #16816802

order	3712
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₂₉×#485

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1856

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);(3,4)(5,8)(6,7)(9,10)(11,12,15,19)(13,16,21,25)(14,17,22,18)(20,23,26,24);(4,7)(8,10)(11,13,15,21)(12,16,19,25)(14,20,22,26)(17,23,18,24);(3,5,6,9)(4,8,7,10)(12,17)(14,22)(16,23)(18,19)(20,26)(24,25)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9240, C₄×C₂₉×#485, C₂₉×#21583, …
maximal normal subgroup of	C₂₉×#9240, C₄×C₂₉×#485, C₂₉×#21583, …
maximal quotient of	C₂×C₂₉×#1825, C₂×C₂₉×#1854, C₂×C₂₉×#1873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1820);

C2×C29×#485 #16816802