C₂×C₃₇×#440 #17991758

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₇×#440

Subgroups

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

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 51 points:

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

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9087, C₃₇×#9090, C₃₇×#9091, …
maximal normal subgroup of	C₃₇×#9087, C₃₇×#9090, C₃₇×#9091, …
maximal quotient of	C₂×C₃₇×SD₁₆⋊C₈, C₂×C₃₇×#1585, C₂×C₃₇×#1588, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1672);

C2×C37×#440 #17991758