C₃₇×#2372 #17991190

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₃₇×#2372

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂²×D₄×C₃₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

560 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 280 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 — 4 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)(38,39,41,40)(43,46)(47,49)(50,51,54,53)(52,56,57,55);(38,40,41,39)(51,53)(55,56);(42,43)(44,47)(45,46)(48,49)(50,52,54,57)(51,55,53,56);(42,44,45,48)(43,47,46,49)(50,53,54,51)(52,56,57,55)

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9439, C₃₇×#9441, C₃₇×#12965, …
maximal normal subgroup of	C₃₇×#9439, C₃₇×#9441, C₃₇×#12965, …
maximal quotient of	C₃₇×#13805, C₃₇×#13816, C₃₇×#13824, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1104);