C₅×#67467 #14278424

order	1920
isoclinism	isoclinic class of #67467
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67467

Splittings

Fitting	C₃×C₅×#334 ⋊ C₂
Hall	C₃×C₅ ⋊ #1360
Sylow	C₃ ⋊ C₅×#1360

Subgroups

	subgroup	G/H
center	C₂²×C₅	#809
commutator	C₂×C₃×C₈	C₂×C₄×C₅
Frattini	C₄×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#334	C₂
socle	C₂²×C₃×C₅	#102
prime radical	C₂×C₅×D₂₄	C₄
cosocle	C₃×C₄×C₈	C₂²×C₅
hypercenter	C₅×#334	D₃
hypocenter	C₃	C₅×#1360
LCS	G ▷ C₂×C₃×C₈ ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₅×#334

204 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4122);