C₃₇×#1451 #17990269

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1451

Subgroups

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

208 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 152 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) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 53 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)(38,39,40,43,41,42,44,45)(47,50)(51,53);(46,47,48,51,49,50,52,53);(39,42)(43,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7164, C₃₇×#7166, C₃₇×#7210, …
maximal normal subgroup of	C₃₇×#7164, C₃₇×#7166, C₃₇×#7210, …
maximal quotient of	C₃₇×#7842, C₃₇×#7848, C₃₇×#8132, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 183);