C₅×#71419 #14312640

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅×C₈ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₅×#71419

Splittings

Hall	C₃×C₅ ⋊ #2108
Sylow	C₃ ⋊ C₅×#2108

Subgroups

	subgroup	G/H
center	C₂×C₅×C₈	C₂²×D₃
commutator	C₂×C₃	C₂×C₄×C₅×C₈
Frattini	C₂×C₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×M₃₂	C₂
socle	C₂²×C₃×C₅	C₂²×C₈
prime radical	C₂³×C₃×C₅	C₂×C₈
cosocle	C₂×C₃×C₈	C₂³×C₅
hypercenter	C₂×C₅×M₃₂	D₃
hypocenter	C₃	C₅×#2108
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂×C₅×M₃₂

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 44 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38338);

C5×#71419 #14312640