C₂×C₃₇×#541 #17992271

order	4736
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₃₇×#541

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
prime radical	C₂⁴×C₃₇	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 5 generators on 63 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63);(5,9)(7,10)(11,12,15,18)(13,16,21,19)(14,22,23,17)(20,25,26,24);(3,4,6,8)(5,7,9,10)(11,12)(13,19)(14,17)(15,18)(16,21)(20,25)(22,23)(24,26);(3,5)(4,7)(6,9)(8,10)(11,13)(12,16)(14,20)(15,21)(17,24)(18,19)(22,25)(23,26);(11,14,15,23)(12,17,18,22)(13,20,21,26)(16,24,19,25)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8327, C₃₇×#8521, C₃₇×#8527, …
maximal normal subgroup of	C₃₇×#8327, C₃₇×#8521, C₃₇×#8527, …
maximal quotient of	C₂×C₃₇×#2314, C₂×C₃₇×#2320, C₂×C₃₇×#2323, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2185);

C2×C37×#541 #17992271