C₂×C₃₇×#383 #17991100

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₃₇×#383

Subgroups

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

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 generators on 59 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59);(3,4,5,6)(9,13)(11,14)(16,19)(17,21);(7,8,10,12)(9,11,13,14)(15,16)(17,20)(18,19)(21,22);(7,9)(8,11)(10,13)(12,14)(15,17,18,21)(16,20,19,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7916, C₂×C₃₇×#1288, C₃₇×#7975, …
maximal normal subgroup of	C₃₇×#7916, C₂×C₃₇×#1288, C₃₇×#7975, …
maximal quotient of	C₂×C₃₇×#1434, C₄×C₃₇×#383, C₂×C₃₇×#1443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1014);

C2×C37×#383 #17991100