#14515302

order	1920
isoclinism	isoclinic class of #14515302
automorphism	Aut(G) = #72240863 (order 23040) · Inn(G) = #11757162 · Out(G) = S₄
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₄²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#11757162
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₂⁵	A₅
LCS	G
UCS	C₁ ◁ C₂

121 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Permutation generators:

(1,2,16)(3,8,13)(4,15,10)(5,6,14)(7,9,11)(17,22,31)(18,36,28)(19,26,37)(20,25,29)(21,35,24)(23,30,38)(27,39,33)(32,40,34);(1,8,16,12,15)(2,14,6,9,10)(3,5,4,11,13)(17,26,29,21,36,20,30,31,18,35)(19,39,28,32,37,23,40,24,27,38)(22,25)(33,34)

Conjugacy classes & character table

14 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₃×#14515302, C₂×#14515302, #72235305, …
maximal subgroup of	#72209668, #72210023, #72210043, …
maximal normal subgroup of	C₃×#14515302, C₂×#14515302, #72235305, …
maximal quotient of	#72209604, #72210023, #72210087, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 241000);