C₅×#67563 #14278485

order	1920
isoclinism	isoclinic class of #67526
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅×#67563

Splittings

Hall	C₃×C₅ ⋊ #1363
Sylow	C₃ ⋊ C₅×#1363

Subgroups

	subgroup	G/H
center	C₂²×C₅	#821
commutator	C₂×C₃×C₈	C₂×C₄×C₅
Frattini	C₄×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₃×C₅	#102
cosocle	C₃×C₄×C₈	C₂²×C₅
hypercenter	C₅×C₄⋊C₁₆	D₃
hypocenter	C₃	C₅×#1363
LCS	G ▷ C₂×C₃×C₈ ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×C₈ ◁ C₅×C₄⋊C₁₆

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

normal subgroups only

This group has 160 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) = 1920

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4183);