C₂×C₃₇×#401 #17991218

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₇×#401

Subgroups

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

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 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)(12,15)(16,17)(19,20,22,24)(21,25,26,23);(3,4,6,8)(5,10,9,7)(11,12,14,15)(13,17,18,16)(19,20)(21,25)(22,24)(23,26);(3,5)(4,7)(6,9)(8,10)(11,13,14,18)(12,16,15,17)(19,21,22,26)(20,23,24,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×C₃₇×#401, C₃₇×#14251, C₃₇×#14333, …
maximal normal subgroup of	C₄×C₃₇×#401, C₃₇×#14251, C₃₇×#14333, …
maximal quotient of	C₂×C₃₇×#1443, C₄×C₃₇×#401, C₃₇×C₂²⋊#401, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1132);

C2×C37×#401 #17991218