C₃₇×#2434 #17991252

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#2434

Subgroups

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

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 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)(43,45)(46,47,50,53)(48,52,49,51);(39,41)(43,45)(46,48,50,49)(47,51,53,52);(38,39)(40,41)(42,43,44,45);(46,49,50,48)(47,52,53,51)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9462, C₃₇×#9949, C₃₇×#9957, …
maximal normal subgroup of	C₃₇×#9462, C₃₇×#9949, C₃₇×#9957, …
maximal quotient of	C₃₇×#13880, C₃₇×#13922, C₃₇×#13976, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1166);

C37×#2434 #17991252