C₅×#68059 #14293516

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

Aliases

direct product

C₅×#68059

Splittings

Fitting	C₃×C₅×C₈² ⋊ C₂
Hall	C₃×C₅ ⋊ #1708
Sylow	C₃ ⋊ C₅×#1708

Subgroups

	subgroup	G/H
center	C₂²×C₅	#874
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×C₈²	C₂
socle	C₂²×C₃×C₅	#127
prime radical	C₅×#874	C₂²
hypercenter	C₅×C₈²	D₃
hypocenter	C₃	C₅×#1708
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×C₈²

380 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 138 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)(6,7,8)(9,10,11,13,12,14,15,16)(18,23)(22,30)(24,28)(25,31);(17,19,20,26,21,27,29,32)(18,22,24,25,23,30,28,31);(7,8)(10,13)(11,15)(14,16)(17,18)(19,25)(20,28)(21,23)(22,26)(24,29)(27,31)(30,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19214);