C₅×#67724 #14278848

order	1920
isoclinism	isoclinic class of #826
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#67724

Splittings

Hall	C₃×C₅ ⋊ #1382
Sylow	C₃ ⋊ C₅×#1382

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	#213
commutator	C₃×C₈	C₄²×C₅
Frattini	C₂²×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#427	C₂
socle	C₂²×C₃×C₅	#102
prime radical	C₂³×C₃×C₅	SD₁₆
cosocle	C₂²×C₃×C₈	C₂²×C₅
hypercenter	C₅×#427	D₃
hypocenter	C₃	C₅×#1382
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₅×#427

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 44 points:

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

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, 4546);

C5×#67724 #14278848