C₅×#78825 #14437776

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₅×#78825

Splittings

Fitting	C₃×C₅×#416 ⋊ C₂
Hall	C₃×C₅ ⋊ #3131
Sylow	C₃ ⋊ C₅×#3131

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5832	C₂
hypercenter	C₅×#416	D₃
hypocenter	C₃	C₅×#3131
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#416

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 163474);

C5×#78825 #14437776