C₂×C₃₇×#432 #17991736

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₇×#432

Subgroups

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

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 2368

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

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

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7863, C₃₇×#7864, C₃₇×#7875, …
maximal normal subgroup of	C₃₇×#7863, C₃₇×#7864, C₃₇×#7875, …
maximal quotient of	C₂×C₃₇×#1745, C₂×C₃₇×#1749, C₂×C₃₇×#1767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1650);

C2×C37×#432 #17991736