C₃₇×#1388 #17990206

order	4736
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1388

Subgroups

	subgroup	G/H
center	C₄×C₃₇	#102
commutator	C₈	C₄²×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂×C₃₇	#340
prime radical	C₂³×C₃₇	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

124 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 2 generators on 69 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)(38,39,42,48,45,50,44,61)(40,51,53,63,56,65,55,69)(41,57,59,66,60,49,43,47)(46,54,62,58,64,68,67,52);(38,40,43,54,44,55,60,52,45,56,59,68,42,53,41,58)(39,46,49,63,48,62,47,65,50,64,57,69,61,67,66,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1388, C₃₇×#12646, C₃₇×#12651, …
maximal normal subgroup of	C₂×C₃₇×#1388, C₃₇×#12646, C₃₇×#12651, …
maximal quotient of	C₃₇×#7158, C₃₇×#7176, C₃₇×#7177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 120);