C₃₇×#261 #14515319

order	1924
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#261

Splittings

Fitting, socle, Hall	C₁₃×C₃₇ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	#261
commutator, hypocenter	C₁₃	C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₇	C₄
prime radical	D₁₃×C₃₇	C₂
cosocle	D₁₃	C₂×C₃₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 481

A minimal faithful permutation representation — 2 generators on 50 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)(39,40,41,43)(42,45,46,50)(44,48,49,47);(38,39,42,45,49,43,47,48,40,44,50,46,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₃₇×#261, C₃₇×C₇⋊#261, C₃₇×#90866, …
maximal normal subgroup of	C₇×C₃₇×#261, C₁₁×C₃₇×#261, C₁₃×C₃₇×#261, …
maximal quotient of	C₇×C₃₇×#261, C₃₇×C₇⋊#261, C₃₇×#90866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1924, 6);

C37×#261 #14515319