C₅×#5113 #11750612

order	960
isoclinism	isoclinic class of #204
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#5113

Splittings

Fitting	C₂²×C₃×C₅×C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ #416
Sylow	C₃ ⋊ C₅×#416

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅	D₁₂
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₅×C₈	D₃
hypocenter	C₃	C₅×#416
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈

316 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 28
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×#68926, C₅×#69789, #14295961, …
maximal normal subgroup of	C₅×#68926, C₅×#69789, #14295961, …
maximal quotient of	C₅×#69734, C₅×#70760, C₅×#70763, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4807);