#72209635

order	9720
isoclinism	isoclinic class of #72209635
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#72209608
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₂×C₃⁴	A₅
LCS	G
UCS	C₁ ◁ C₂

170 conjugacy classes of subgroups; only the 5 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 5 normal subgroups are shown.

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

Full subgroup data →

Presentation

Permutation generators:

(1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,32)(28,31)(30,35)(36,38)(37,39);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(26,29,30)(31,34,37)(32,33,36);(25,27,28)(26,31,32)(29,33,34)(30,36,37)(35,38,39);(25,27,28)(26,32,31)(29,34,33)(30,36,37)(35,38,39);(25,27,28)(26,32,31)(29,33,34)(30,37,36)(35,38,39);(25,28,27)(26,32,31)(29,33,34)(30,36,37)(35,38,39)

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72228153
maximal quotient of	#72209948

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,2,5,3)(4,7,6,8)(9,13,11,14)(10,15,12,16)(17,19,18,20)(21,24,23,22)(25,26)(27,32)(28,31)(30,35)(36,38)(37,39), (1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(26,29,30)(31,34,37)(32,33,36), (25,27,28)(26,31,32)(29,33,34)(30,36,37)(35,38,39), (25,27,28)(26,32,31)(29,34,33)(30,36,37)(35,38,39), (25,27,28)(26,32,31)(29,33,34)(30,37,36)(35,38,39), (25,28,27)(26,32,31)(29,33,34)(30,36,37)(35,38,39));