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C3×#66245 #11756802

order960
isoclinismisoclinic class of (C24⋊C5)⋊C2
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#66245

Splittings

derivedC24⋊C5 ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC2×C3(C24⋊C5)⋊C2
commutator, hypocenterC24⋊C5C3×C4
FrattiniC2C3×(C24⋊C5)⋊C2
Fitting, socleC25×C3D5
prime radicalC2×C3×C24⋊C5C2
cosocleC2×C24⋊C5C2×C3
LCSG ▷ C24⋊C5
UCSC1 ◁ C2×C3

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 60

A minimal faithful permutation representation — 2 generators on 17 points:

(1,2,3)(4,5,6,7)(9,11,13,14)(12,17,16,15);(8,9,12,15,11)(10,13,16,17,14)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#10619374, C3×(C24⋊C5)⋊Q8, C3×C4×(C24⋊C5)⋊C2, …
maximal normal subgroup ofC3×#10619374, C3×(C24⋊C5)⋊Q8, C3×C4×(C24⋊C5)⋊C2, …
maximal quotient ofC3×#10617015, C3×#10617016, C3×#10617017, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10997);