#72209602

order	3840
isoclinism	isoclinic class of #72209602
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Fitting

C₂⁶ ⋊ A₅

Subgroups

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

1043 conjugacy classes of subgroups; only the 7 normal subgroups are shown.

normal subgroups only

This group has 1043 conjugacy classes of subgroups — too many to draw. Only its 7 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)(3,10)(4,9)(5,7)(6,8)(11,18)(12,16)(13,17);(1,3,2)(4,13,9)(5,11,7)(6,12,8)(10,14,15)(16,19,24)(17,20,22)(18,21,23);(1,4)(2,7)(3,11)(5,6)(8,9)(10,16)(12,13)(14,19)(15,22)(17,18)(20,21)(23,24);(1,5)(2,8)(3,12)(4,6)(7,9)(10,17)(11,13)(14,20)(15,23)(16,18)(19,21)(22,24);(1,5)(2,9)(3,12)(4,6)(7,8)(10,18)(11,13)(14,19)(15,22)(16,17)(20,21)(23,24);(1,6)(2,7)(3,13)(4,5)(8,9)(10,16)(11,12)(14,20)(15,23)(17,18)(19,21)(22,24);(1,5)(2,7)(3,11)(4,6)(8,9)(10,18)(12,13)(14,21)(15,23)(16,17)(19,20)(22,24);(1,4)(2,9)(3,13)(5,6)(7,8)(10,17)(11,12)(14,20)(15,22)(16,18)(19,21)(23,24)

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72242443, #72244262, #72256798, …
maximal quotient of	#72209624, #72209632, #72235040, …

GAP

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

gap> G := Group((1,2)(3,10)(4,9)(5,7)(6,8)(11,18)(12,16)(13,17), (1,3,2)(4,13,9)(5,11,7)(6,12,8)(10,14,15)(16,19,24)(17,20,22)(18,21,23), (1,4)(2,7)(3,11)(5,6)(8,9)(10,16)(12,13)(14,19)(15,22)(17,18)(20,21)(23,24), (1,5)(2,8)(3,12)(4,6)(7,9)(10,17)(11,13)(14,20)(15,23)(16,18)(19,21)(22,24), (1,5)(2,9)(3,12)(4,6)(7,8)(10,18)(11,13)(14,19)(15,22)(16,17)(20,21)(23,24), (1,6)(2,7)(3,13)(4,5)(8,9)(10,16)(11,12)(14,20)(15,23)(17,18)(19,21)(22,24), (1,5)(2,7)(3,11)(4,6)(8,9)(10,18)(12,13)(14,21)(15,23)(16,17)(19,20)(22,24), (1,4)(2,9)(3,13)(5,6)(7,8)(10,17)(11,12)(14,20)(15,22)(16,18)(19,21)(23,24));