C₃₇×#3038 #17991856

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3038

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

584 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 49 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)(43,47)(44,45)(48,49);(38,39,40,41);(42,43)(44,47)(45,49)(46,48);(42,44,46,45)(43,47,48,49)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9173, C₃₇×#9174, C₃₇×#9318, …
maximal normal subgroup of	C₃₇×#9173, C₃₇×#9174, C₃₇×#9318, …
maximal quotient of	C₃₇×#19266, C₃₇×#19267, C₃₇×#19268, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1770);