C₅×#71969 #14294558

order	1920
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅ · Schur multiplier (H₂) = C₂³×C₄

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#71969

Splittings

Hall	C₃×C₅ ⋊ #1735
Sylow	C₃ ⋊ C₅×#1735

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₅	D₁₂
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂³×C₃×C₅×C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂³×C₅×C₈	D₃
hypocenter	C₃	C₅×#1735
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 20256);

C5×#71969 #14294558