C₃×#64985 #11749593

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃×#64985

Splittings

Fitting	C₃×C₄×C₅×C₈ ⋊ C₂
Hall	C₃×C₅ ⋊ #495
Sylow	C₅ ⋊ C₃×#495

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂³×C₃
Frattini	C₂×C₄	C₂²×C₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂×D₄
prime radical	C₂×C₃×D₄₀	C₂
hypercenter	C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×#495
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈

260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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)(4,5,7,8,6)(13,15,16,22,17,23,25,28)(14,19,20,21,18,26,24,27);(9,10,11,12)(14,18)(19,26)(20,24)(21,27);(5,6)(7,8)(10,12)(13,14)(15,21)(16,24)(17,18)(19,22)(20,25)(23,27)(26,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10597958, C₃×#10598053, #14278437, …
maximal normal subgroup of	C₃×#10597958, C₃×#10598053, #14278437, …
maximal quotient of	C₃×#10598851, C₃×#10598856, C₃×#10598852, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3788);