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Cayley diagram

C4×C24⋊C5 #66246

order320
isoclinismisoclinic class of C24⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC4×C24⋊C5
unambiguous semidirect product(C24×C4)⋊C5

Splittings

Fitting, SylowC24×C4 ⋊ C5
derivedC24 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4C24⋊C5
commutator, hypocenterC24C4×C5
FrattiniC2C2×C24⋊C5
FittingC24×C4C5
socle, cosocleC25C2×C5
prime radicalC2×C24⋊C5C2
LCSG ▷ C24
UCSC1 ◁ C4

147 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 14
transitive degreeμt(G) = 20

A minimal faithful permutation representation — 2 generators on 14 points:

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

derived subgroup of#13046147, #13046148, #13046149, …
maximal subgroup of#10617015, C8×C24⋊C5, (C24⋊C5)⋊Q8, …
maximal normal subgroup of#10617015, C8×C24⋊C5, (C24⋊C5)⋊Q8, …
maximal quotient ofC4×2−1+4⋊C5, C8×C24⋊C5, #3573⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1584);