C₃₇×#1382 #17990200

order	4736
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄²×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1382

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	D₈
commutator	C₈	C₄²×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂²×C₃₇	#102
prime radical	C₂³×C₃₇	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

132 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 73
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 73 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)(38,39,40,41)(42,43)(44,53)(45,58)(46,61)(47,63)(48,52)(49,54)(50,60)(51,59)(55,65)(56,73)(57,69)(62,66)(64,72)(67,71)(68,70);(42,44,46,55,59,70,60,71,48,57,45,54,47,56,62,72)(43,49,50,53,63,67,61,73,52,65,66,69,51,64,58,68)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#1382, C₃₇×#12561, C₄×C₃₇×#359, …
maximal normal subgroup of	C₂×C₃₇×#1382, C₃₇×#12561, C₄×C₃₇×#359, …
maximal quotient of	C₃₇×#7155, C₃₇×#7171, C₃₇×#7172, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 114);