C₅×#68201 #14289289

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#68201

Splittings

Fitting	C₃×C₅×D₄⋊C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ #1628
Sylow	C₃ ⋊ C₅×#1628

Subgroups

	subgroup	G/H
center	C₂²×C₅	#882
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×D₄⋊C₈	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5015	C₂
hypercenter	C₅×D₄⋊C₈	D₃
hypocenter	C₃	C₅×#1628
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×D₄⋊C₈

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 14987);

C5×#68201 #14289289