C₅×#67718 #14277654

order	1920
isoclinism	isoclinic class of #4537
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#67718

Splittings

Hall	C₃×C₅ ⋊ #1323
Sylow	C₃ ⋊ C₅×#1323

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	#217
commutator	C₂×C₃×C₄	C₂×C₅×C₈
Frattini	C₂²×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₂²⋊C₈
prime radical	C₂³×C₃×C₅	M₁₆
cosocle	C₂²×C₃×C₈	C₂²×C₅
hypercenter	C₅×#424	D₃
hypocenter	C₃	C₅×#1323
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₅×#424

188 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 48
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5)(6,7,8)(9,11,12,16)(10,13,14,15)(17,19)(18,24)(20,33)(21,35)(22,30)(23,32)(25,41)(26,43)(27,29)(28,40)(31,37)(34,47)(36,38)(39,45)(42,46)(44,48);(7,8)(9,10)(11,15,16,13)(12,14)(17,18,21,26,22,27,36,44,23,28,37,45,20,25,34,42)(19,29,31,46,30,40,47,43,32,41,35,48,33,24,38,39)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 3352);