#72209735

order	17280
isoclinism	isoclinic class of #72209735
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	#72209614
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₂⁴×C₃	A₆
LCS	G
UCS	C₁ ◁ C₃

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

normal subgroups only

This group has 284 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:

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72227477, #72227488, #72227492

GAP

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

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