C₃×C₆₁×D₃₇ #27214362

order	13542
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₆₁×D₃₇

Splittings

Fitting, socle, Hall	C₃×C₃₇×C₆₁ ⋊ C₂
derived, Sylow	C₃₇ ⋊ C₂×C₃×C₆₁
Hall	C₃₇×C₆₁ ⋊ C₂×C₃
Hall	C₃×C₃₇ ⋊ C₂×C₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₆₁	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₃₇×C₆₁	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₃×C₆₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 6771

A minimal faithful permutation representation — 2 generators on 101 points:

(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)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98)(99,100,101);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₆₁×#3866, C₃×#22583261, C₃×D₃₇×D₆₁, …
maximal normal subgroup of	C₃×C₆₁×#3866, C₃×#22583261, C₃×D₃₇×D₆₁, …
maximal quotient of	C₃×C₆₁×Dic₃₇, C₂×C₃×C₆₁×D₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13542, 7);

C3×C61×D37 #27214362