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C2×((C24⋊C5)⋊C2)⋊C3 #11757165

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

Aliases

direct productC2×((C24⋊C5)⋊C2)⋊C3
unambiguous semidirect product((C24⋊C5)⋊C2)⋊(C2×C3)
unambiguous semidirect productAGL(1,𝔽16)⋊C22
unambiguous semidirect product(C2×(C24⋊C5)⋊C2)⋊C3
unambiguous semidirect product(C2×AGL(1,𝔽16))⋊C2

Splittings

Fitting, socleC25 ⋊ C3×D5
derivedC24⋊C5 ⋊ C22×C3
HallC2×(C24⋊C5)⋊C2 ⋊ C3

Subgroups

subgroupG/H
center, hypercenterC2((C24⋊C5)⋊C2)⋊C3
commutator, cosocle, hypocenterC24⋊C5C22×C3
FrattiniC1G
Fitting, socleC25C3×D5
LCSG ▷ C24⋊C5
UCSC1 ◁ C2

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×((C24⋊C5)⋊C2)⋊C3, C4⋊(((C24⋊C5)⋊C2)⋊C3), (C22⋊((C24⋊C5)⋊C2))⋊C3, …
maximal normal subgroup ofC4×((C24⋊C5)⋊C2)⋊C3, C4⋊(((C24⋊C5)⋊C2)⋊C3), (C22⋊((C24⋊C5)⋊C2))⋊C3, …
maximal quotient ofAGL(1,𝔽16)⋊Q8, C4×((C24⋊C5)⋊C2)⋊C3, C4⋊(((C24⋊C5)⋊C2)⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11360);