C₅×#83411 #14424534

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅×#83411

Splittings

Fitting	C₃×C₅×#536 ⋊ C₂
Hall	C₃×C₅ ⋊ #3011
Sylow	C₃ ⋊ C₅×#3011

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#536	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#1010	C₂
hypercenter	C₅×#536	D₃
hypocenter	C₃	C₅×#3011
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₅×#536

1400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 4 generators on 44 points:

(1,2,3,4,5)(6,7,8)(16,27)(20,34)(24,38)(28,40)(32,43)(35,41)(37,44)(39,42);(10,12)(13,16)(14,20)(15,24)(17,28)(18,27)(19,32)(21,35)(22,34)(23,37)(25,39)(26,38)(29,41)(30,42)(31,40)(33,43)(36,44);(7,8)(13,15,18,26)(14,19,22,33)(16,24,27,38)(17,30,31,25)(20,32,34,43)(21,36,29,23)(28,42,40,39)(35,44,41,37);(9,10)(11,12)(13,14,18,22)(15,23,26,36)(16,20,27,34)(17,29,31,21)(19,30,33,25)(24,37,38,44)(28,41,40,35)(32,42,43,39)

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, 150232);

C5×#83411 #14424534