C₃₇×#1450 #17990268

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

Aliases

direct product

C₃₇×#1450

Subgroups

	subgroup	G/H
center	C₄×C₈×C₃₇	C₂²
commutator	C₂	C₂×C₄×C₈×C₃₇
Frattini, cosocle	C₄²	C₂³×C₃₇
socle	C₂²×C₃₇	C₂×C₄²
prime radical	C₂³×C₃₇	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₃₇ ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(46,47,49,52,50,53,56,59)(48,51,55,58,54,57,60,61);(38,39,40,42,41,43,44,45)(46,48)(47,51)(49,55)(50,54)(52,58)(53,57)(56,60)(59,61);(48,54)(51,57)(55,60)(58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7140, C₃₇×#7141, C₃₇×#7153, …
maximal normal subgroup of	C₃₇×#7140, C₃₇×#7141, C₃₇×#7153, …
maximal quotient of	C₃₇×#7841, C₃₇×#7849, C₃₇×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 182);

C37×#1450 #17990268