#72209678

order	14580
isoclinism	isoclinic class of #72209678
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

Fitting

C₃⁵ ⋊ A₅

Subgroups

	subgroup	G/H
center, Frattini, socle, hypercenter	C₃	#72209608
commutator, hypocenter	G	C₁
Fitting, cosocle	C₃⁵	A₅
LCS	G
UCS	C₁ ◁ C₃

385 conjugacy classes of subgroups; only the 4 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 4 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)(3,8)(4,7)(5,6)(9,14)(10,13);(1,3,2)(4,10,7)(5,9,6)(8,11,12)(13,16,17)(14,15,18);(1,4,5)(2,6,7)(3,9,10)(12,17,18);(1,5,4)(2,6,7)(3,10,9)(8,13,14);(1,4,5)(3,10,9)(8,14,13)(12,18,17);(1,5,4)(2,7,6)(8,14,13)(12,17,18);(1,5,4)(2,6,7)(3,9,10)(8,14,13)(11,15,16)(12,18,17)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72209948

GAP

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

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