C₂×C₃₇×#471 #17991882

order	4736
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₇×#471

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×AGL(1,ℤ/8)×C₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1184

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);(4,8)(5,11)(6,14)(10,16)(12,13)(15,17);(3,4,6,8,7,10,14,16)(5,9,12,15,13,18,11,17);(3,5)(4,9)(6,12)(7,13)(8,15)(10,18)(11,14)(16,17)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₃₇×#471, C₃₇×#21557, C₃₇×#23044, …
maximal normal subgroup of	C₄×C₃₇×#471, C₃₇×#21557, C₃₇×#23044, …
maximal quotient of	C₂×C₃₇×#1665, C₂×C₃₇×#1671, C₂×C₃₇×#1681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1796);

C2×C37×#471 #17991882