C₂×C₃₇×#346 #17990924

order	4736
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×C₃₇×#346

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₃₇	C₂²
commutator	C₂	C₂×C₄×C₈×C₃₇
Frattini, cosocle	C₂×C₈	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₇ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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);(7,8,9,13,10,14,15,20,11,12,16,18,17,19,21,22);(3,4,5,6)(8,12)(13,18)(14,19)(20,22)

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7137, C₃₇×#7140, C₃₇×#7156, …
maximal normal subgroup of	C₃₇×#7137, C₃₇×#7140, C₃₇×#7156, …
maximal quotient of	C₂×C₃₇×#1311, C₂×C₃₇×#1312, C₃₇×#11408, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 838);

C2×C37×#346 #17990924