C₅×#71297 #14293558

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₅×#71297

Splittings

Fitting	C₃×C₅×#494 ⋊ C₂
Hall	C₃×C₅ ⋊ #1709
Sylow	C₃ ⋊ C₅×#1709

Subgroups

	subgroup	G/H
center	C₂²×C₅	#940
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#494	C₂
socle	C₂²×C₃×C₅	#127
prime radical	C₅×#4695	C₂
hypercenter	C₅×#494	D₃
hypocenter	C₃	C₅×#1709
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#494

424 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 130 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 — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19256);