C₃₇×#2365 #17991183

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2365

Subgroups

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

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 4736

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)(39,41)(42,43,45,44)(47,50)(51,52);(42,44,45,43)(46,47)(48,52)(49,50)(51,53);(38,39,40,41);(46,48,49,53)(47,51,50,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8922, C₃₇×#8923, C₃₇×#8925, …
maximal normal subgroup of	C₃₇×#8922, C₃₇×#8923, C₃₇×#8925, …
maximal quotient of	C₄⋊C₄²×C₃₇, C₃₇×#13817, C₃₇×#13821, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1097);

C37×#2365 #17991183