#14515303

order	1920
isoclinism	isoclinic class of #14515303
automorphism	Aut(G) = #72240876 (order 7680) · Inn(G) = G · Out(G) = C₂²
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Frattini, Fitting, cosocle	C₂⁵	A₅
socle	C₂⁴	SL(2,𝔽₅)
LCS	G
UCS	C₁

73 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

14 conjugacy classes — view the full character table.

Relationships

derived subgroup of	C₃×#14515303, #72235209, C₂×#14515303, …
maximal subgroup of	#72209669, #72210011, #72210023, …
maximal normal subgroup of	C₃×#14515303, #72235209, C₂×#14515303, …
maximal quotient of	#72209605, #72210065, #72213660, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 241001);