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C2×C4×C22⋊(C13⋊C3) #11929259

order1248
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×C4×C22⋊(C13⋊C3)
unambiguous semidirect product(C23×C4)⋊(C13⋊C3)
unambiguous semidirect product(C2×C4×C13)⋊A4

Splittings

Fitting, HallC23×C4×C13 ⋊ C3
derivedC22×C13 ⋊ C2×C3×C4
SylowC23×C4 ⋊ C13⋊C3
SylowC13 ⋊ C2×C4×A4

Subgroups

subgroupG/H
center, hypercenterC2×C4C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C2×C3×C4
FrattiniC2C22×C22⋊(C13⋊C3)
FittingC23×C4×C13C3
socleC24×C13C2×C3
prime radicalC22×C22⋊(C13⋊C3)C2
cosocleC23×C13C22×C3
LCSG ▷ C22×C13
UCSC1 ◁ C2×C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 312

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1371);