C₅×#4904 #11750403

order	960
isoclinism	isoclinic class of D₄₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅×#4904

Splittings

Fitting	C₂×C₃×C₅×C₁₆ ⋊ C₂
Hall	C₃×C₅ ⋊ #508
Sylow	C₃ ⋊ C₅×#508

Subgroups

	subgroup	G/H
center	C₄×C₅	D₂₄
commutator, cosocle	C₃×C₈	C₂³×C₅
Frattini	C₈	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	C₂×D₈
hypercenter	C₂×C₅×C₁₆	D₃
hypocenter	C₃	C₅×#508
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₂×C₅×C₁₆

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 40
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#67585, C₅×#67598, #14279614, …
maximal normal subgroup of	C₅×#67585, C₅×#67598, #14279614, …
maximal quotient of	C₅×#71412, C₅×#71404, C₄×C₅×D₄₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4598);