Finite Group Databasebeta

← Prev (#11757160) Next (#11757162) →

C24×A5 #11757161

order960
isoclinismisoclinic class of A5
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC24×A5

Subgroups

subgroupG/H
center, Fitting, hypercenterC24A5
commutator, hypocenterA5C24
FrattiniC1G
LCSG ▷ A5
UCSC1 ◁ C24

1913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC22⋊A4×A5, A5×C24⋊C5, A5×#120⋊C3
socle ofC23×A5⋊C4, C23×C4×A5, C24×S5, …
maximal subgroup ofC2×C22⋊(A5⋊C4), C2×C22⋊C4×A5, #14514809, …
maximal normal subgroup ofC2×C22⋊(A5⋊C4), C2×C22⋊C4×A5, #14514809, …
maximal quotient ofC23×C4×A5, C22×D4×A5, C22×Q8×A5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11356);