C₂×C₃₇×#525 #17992253

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₃₇×#525

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
socle	C₂³×C₃₇	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

1880 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(5,6)(7,8)(9,12)(10,11)(13,14);(8,11)(12,14);(4,6);(7,9,10,13)(8,12,11,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8331, C₃₇×#10971, C₃₇×#10993, …
maximal normal subgroup of	C₃₇×#8331, C₃₇×#10971, C₃₇×#10993, …
maximal quotient of	C₂×C₃₇×#2280, C₂×C₃₇×#2290, C₂×C₃₇×#2296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2167);

C2×C37×#525 #17992253