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A4×C43×C49 #38760261

order25284
automorphism?
homologyAbelianization (H1) = C3×C43×C49 · Schur multiplier (H2) = C2

Aliases

direct productA4×C43×C49
unambiguous semidirect productC22⋊(C3×C43×C49)

Splittings

Fitting, HallC22×C43×C49 ⋊ C3
derived, SylowC22 ⋊ C3×C43×C49
HallC22×C49 ⋊ C3×C43
HallC22×C43 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC43×C49A4
commutator, hypocenterC22C3×C43×C49
FrattiniC7C7×A4×C43
FittingC22×C43×C49C3
socleC22×C7×C43C3×C7
prime radicalC7×A4×C43C7
cosocleC22×C7C3×C7×C43
LCSG ▷ C22
UCSC1 ◁ C43×C49

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8428

Conjugacy classes & character table

8428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 68);