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C4×Q8⋊(C13⋊C3) #11928751

order1248
isoclinismisoclinic class of Q8⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC4×Q8⋊(C13⋊C3)
unambiguous semidirect product(C4×Q8)⋊(C13⋊C3)
unambiguous semidirect product(C4×C13)⋊SL(2,𝔽3)

Splittings

Fitting, HallC4×Q8×C13 ⋊ C3
derivedQ8×C13 ⋊ C3×C4
SylowC4×Q8 ⋊ C13⋊C3
SylowC13 ⋊ C4×SL(2,𝔽3)

Subgroups

subgroupG/H
center, hypercenterC2×C4C22⋊(C13⋊C3)
commutator, hypocenterQ8×C13C3×C4
FrattiniC22C2×C22⋊(C13⋊C3)
FittingC4×Q8×C13C3
socleC22×C13C2×A4
prime radicalC2×Q8⋊(C13⋊C3)C2
cosocleC2×Q8×C13C2×C3
LCSG ▷ Q8×C13
UCSC1 ◁ C2×C4

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 863);