C₂×C₃₇×#464 #17991852

order	4736
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₇×#464

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 59 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(4,6)(7,8)(9,15)(10,12)(11,19)(13,17)(14,18)(16,22)(20,21);(3,4,5,6)(8,12)(13,21)(14,19)(15,22);(7,9,10,16)(8,13,12,21)(11,20,18,17)(14,22,19,15)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9244, C₄×C₃₇×#464, C₃₇×#21508, …
maximal normal subgroup of	C₃₇×#9244, C₄×C₃₇×#464, C₃₇×#21508, …
maximal quotient of	C₂×C₃₇×#1678, C₂×C₃₇×#1680, C₂×C₃₇×#1682, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1766);

C2×C37×#464 #17991852