#72209604

order	3840
isoclinism	isoclinic class of #72209604
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂²	#11757162
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂⁶	A₅
LCS	G
UCS	C₁ ◁ C₂²

408 conjugacy classes of subgroups; only the 8 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 8 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)(27,30)(28,29)(31,34);(1,4,2)(3,5,6)(7,9,10)(8,11,12)(13,16,17)(14,15,18)(19,21,22)(20,23,24)(25,27,26)(28,31,29)(30,32,33)(34,35,36);(1,5)(2,3)(4,6)(7,8)(9,11)(10,12)(13,14)(15,16)(17,18)(19,20)(21,23)(22,24);(26,29)(27,31)(30,34)(32,35);(25,28)(26,29)(27,31)(33,36);(25,28)(27,31)(30,34)(32,35);(25,28)(26,29)(30,34)(33,36);(25,28)(26,29)(27,31)(30,34)(32,35)(33,36)

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72209937, #72249859, #72256821, …
maximal quotient of	#72209630, #72209632, #72235739, …

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