C₃₇×#1181 #16864279

order	4292
isoclinism	isoclinic class of #1181
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#1181

Splittings

Fitting, socle, Hall	C₂₉×C₃₇ ⋊ C₄
derived, Sylow	C₂₉ ⋊ C₄×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	#1181
commutator, hypocenter	C₂₉	C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₂₉×C₃₇	C₄
prime radical	C₃₇×D₂₉	C₂
cosocle	D₂₉	C₂×C₃₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 1073

A minimal faithful permutation representation — 2 generators on 66 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)(42,45,46,52)(44,49,50,48)(47,54,55,62)(51,58,59,60)(53,61,56,57)(63,65,66,64);(38,39,42,47,56,52,60,54,63,65,61,49,40,44,51,59,50,43,48,57,64,66,62,58,45,53,55,46,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇⋊C₃×#1181, C₃×C₃₇×#1181, C₃₇×C₃⋊#1181, …
maximal normal subgroup of	C₃₇⋊C₃×#1181, C₃×C₃₇×#1181, C₅×C₃₇×#1181, …
maximal quotient of	C₃×C₃₇×#1181, C₃₇×C₃⋊#1181, C₅×C₃₇×#1181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4292, 7);

C37×#1181 #16864279