C₅×#78573 #14417546

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅×#78573

Splittings

Hall	C₃×C₅ ⋊ #2950
Sylow	C₃ ⋊ C₅×#2950

Subgroups

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#2950
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

912 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)(14,21)(16,27)(19,33)(22,29)(23,36)(24,38)(28,40)(39,42);(9,11,12,10)(13,16,18,27)(14,20,21,35)(15,24,26,38)(17,28,31,40)(19,32,33,43)(22,34,29,41)(23,37,36,44)(25,39,30,42);(7,8)(13,15,18,26)(14,19,21,33)(16,24,27,38)(17,30,31,25)(20,32,35,43)(22,36,29,23)(28,42,40,39)(34,44,41,37);(7,8)(9,10,12,11)(13,14)(15,23)(16,20)(17,29)(18,21)(19,25)(22,31)(24,37)(26,36)(27,35)(28,41)(30,33)(32,39)(34,40)(38,44)(42,43)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143244);

C5×#78573 #14417546