C₃₇×#1464 #17990282

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1464

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
prime radical	C₂⁴×C₃₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

252 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 1184

A minimal faithful permutation representation — 3 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)(38,39,40,43,41,42,44,45)(46,47)(48,54,56,51)(49,52)(50,53)(55,60,61,58)(57,59);(46,48)(47,51)(49,55)(50,56)(52,58)(53,54)(57,61)(59,60);(39,42)(43,45)(46,49,50,57)(47,52,53,59)(48,55,56,61)(51,58,54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7214, C₃₇×#7216, C₃₇×#7325, …
maximal normal subgroup of	C₃₇×#7214, C₃₇×#7216, C₃₇×#7325, …
maximal quotient of	C₃₇×#7608, C₃₇×#7611, C₃₇×#7614, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 196);