C₃₇×#2247 #17991065

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#2247

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 73 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)(42,43,47,51)(44,52,56,68)(45,57,59,72)(46,60,58,50)(48,61,63,54)(49,64,65,53)(55,71,70,67)(62,69,66,73);(42,44,53,69,46,55,59,61,47,56,64,73,58,70,45,54)(43,48,57,67,50,62,65,68,51,63,72,71,60,66,49,52);(38,39,40,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7445, C₃₇×#7449, C₃₇×#12322, …
maximal normal subgroup of	C₃₇×#7445, C₃₇×#7449, C₃₇×#12322, …
maximal quotient of	C₃₇×#12504, C₃₇×#12510, C₃₇×#12516, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 979);

C37×#2247 #17991065