C₃₇×#1389 #17990207

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

Aliases

direct product

C₃₇×#1389

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	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

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

normal subgroups only

This group has 128 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)(38,39,42,47,44,48,43,59)(40,49,51,66,54,62,53,68)(41,55,56,64,58,69,57,46)(45,60,61,52,63,67,65,50);(38,40,41,52,42,51,56,67,44,54,58,50,43,53,57,60)(39,45,46,62,59,65,69,66,48,63,64,49,47,61,55,68)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1389, C₃₇×#12646, C₃₇×#12649, …
maximal normal subgroup of	C₂×C₃₇×#1389, C₃₇×#12646, C₃₇×#12649, …
maximal quotient of	C₃₇×#7159, C₃₇×#7175, C₃₇×#7177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 121);