C₃₇×#3520 #17992338

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3520

Subgroups

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

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(38,39,42,43)(40,44,45,41)(47,50)(51,53);(39,43)(41,44);(38,40)(39,41)(42,45)(43,44)(46,47)(48,51)(49,50)(52,53);(38,41)(39,40)(42,44)(43,45);(38,40)(39,41)(42,45)(43,44)(46,48,49,52)(47,51,50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8418, C₃₇×#17548, C₃₇×#17598, …
maximal normal subgroup of	C₃₇×#8418, C₃₇×#17548, C₃₇×#17598, …
maximal quotient of	C₃₇×#34194, C₃₇×#34233, C₃₇×#34235, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2252);

C37×#3520 #17992338