C₅×#4772 #11750271

order	960
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅×#4772

Splittings

Fitting	C₃×C₅×#102 ⋊ C₂
Hall	C₃×C₅ ⋊ #416
Sylow	C₃ ⋊ C₅×#416

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#102	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#237	C₂
cosocle	C₂×C₃×C₄	C₂³×C₅
hypercenter	C₅×#102	D₃
hypocenter	C₃	C₅×#416
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#102

316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 110 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)(13,15,16,24,18,25,17,23)(14,20,21,27,19,26,22,28);(14,19)(15,23)(16,17)(20,27)(24,25)(26,28);(7,8)(13,14)(15,20)(16,21)(17,22)(18,19)(23,28)(24,27)(25,26)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#416, C₂×C₅×#4772, D₅×#4772, …
maximal normal subgroup of	C₅×D₃×#416, C₂×C₅×#4772, D₅×#4772, …
maximal quotient of	C₅×#68165, C₅×#68169, C₅×#68173, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4466);