C₃₇×#3483 #17992301

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3483

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
socle	C₂²×C₃₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 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 — 5 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)(39,43)(44,45)(46,47)(48,51)(49,53)(50,52);(38,39,42,43)(40,44,41,45)(46,48,51,47)(49,53,50,52);(38,40,42,41)(39,44,43,45)(46,49,51,50)(47,52,48,53);(38,40,42,41)(39,45,43,44)(46,50,51,49)(47,52,48,53);(38,41,42,40)(39,45,43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8441, C₃₇×#12773, C₃₇×#17520, …
maximal normal subgroup of	C₃₇×#8441, C₃₇×#12773, C₃₇×#17520, …
maximal quotient of	C₃₇×#34129, C₃₇×#34155, C₄×C₃₇×#550, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2215);