C₃₇×#2984 #17991802

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#2984

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

364 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 272 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) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 61 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)(38,39,42,43,41,45,40,44)(46,47)(48,54)(49,52)(50,53)(51,56)(55,60)(57,59)(58,61);(38,40,41,42)(39,43,45,44)(46,48,50,56)(47,51,53,54)(49,57,58,55)(52,60,61,59);(38,40,41,42)(39,44,45,43)(46,49,50,58)(47,52,53,61)(48,55,56,57)(51,59,54,60);(39,45)(43,44)(47,53)(51,54)(52,61)(59,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9164, C₃₇×#9166, C₃₇×#9244, …
maximal normal subgroup of	C₃₇×#9164, C₃₇×#9166, C₃₇×#9244, …
maximal quotient of	C₃₇×#20535, C₃₇×#20572, C₃₇×#20573, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1716);