C₅×#67802 #14278530

order	1920
isoclinism	isoclinic class of #67774
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67802

Splittings

Hall	C₃×C₅ ⋊ #1365
Sylow	C₃ ⋊ C₅×#1365

Subgroups

	subgroup	G/H
center	C₂²×C₅	#832
commutator	C₂×C₃×C₈	C₂×C₄×C₅
Frattini	C₄×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#500	C₂
socle, prime radical	C₂²×C₃×C₅	#102
cosocle	C₃×C₄×C₈	C₂²×C₅
hypercenter	C₅×#500	D₃
hypocenter	C₃	C₅×#1365
LCS	G ▷ C₂×C₃×C₈ ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₅×#500

172 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4228);