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C5×#4822 #11750321

order960
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#4822

Splittings

FittingC3×C5×#104 ⋊ C2
HallC3×C5 ⋊ #453
SylowC3 ⋊ C5×#453

Subgroups

subgroupG/H
centerC2×C5#882
commutator, cosocleC2×C3×C4C23×C5
FrattiniC2×C4C22×C5×D3
FittingC3×C5×#104C2
socleC2×C3×C5#120
hypercenterC5×#104D3
hypocenterC3C5×#453
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#104

336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2,3,4,5)(6,7,8)(10,13,14,15);(9,10)(11,13)(12,14)(15,16);(7,8)(11,16)(13,15)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×#453, C2×C5×#4822, D5×#4822, …
maximal normal subgroup ofC5×D3×#453, C2×C5×#4822, D5×#4822, …
maximal quotient ofC5×#68284, C5×#68316, C5×#68285, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4516);