C₃₇×#1387 #17990205

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

Aliases

direct product

C₃₇×#1387

Subgroups

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

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

normal subgroups only

This group has 136 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) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 57 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)(43,47)(44,51)(45,52)(48,50)(49,56)(53,57)(54,55);(42,43,44,48,52,54,57,55,46,50,53,47,45,49,51,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1387, C₃₇×#12569, C₄×C₃₇×#361, …
maximal normal subgroup of	C₂×C₃₇×#1387, C₃₇×#12569, C₄×C₃₇×#361, …
maximal quotient of	C₃₇×#7159, C₃₇×#7176, C₃₇×#7178, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 119);