C₂×C₃₇×#472 #17991883

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×#472

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

488 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)(5,12)(6,9)(11,16)(13,14)(15,17);(3,4,9,16,7,11,6,8)(5,10,12,17,14,18,13,15);(3,5)(4,10)(6,13)(7,14)(8,15)(9,12)(11,18)(16,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12996, C₃₇×#13007, C₃₇×#13068, …
maximal normal subgroup of	C₃₇×#12996, C₃₇×#13007, C₃₇×#13068, …
maximal quotient of	C₂×C₃₇×#1667, C₂×C₃₇×#1675, C₂×C₃₇×#1677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1797);

C2×C37×#472 #17991883