Finite Group Databasebeta

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C3×C22⋊#10625202 #22580381

order8892
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C22⋊#10625202
unambiguous semidirect product(C22×C3)⋊#10625202

Splittings

Fitting, socleC22×C3×C13×C19 ⋊ C3
derived, HallC22×C13×C19 ⋊ C32
HallC13×C19 ⋊ C3×A4
HallC22×C19 ⋊ C3×C13⋊C3
HallC22×C13 ⋊ C3×C19⋊C3
SylowC19 ⋊ C3×C22⋊(C13⋊C3)
SylowC13 ⋊ C3×C22⋊(C19⋊C3)
SylowC22 ⋊ C3×#10625202

Subgroups

subgroupG/H
center, hypercenterC3C22⋊#10625202
commutator, hypocenterC22×C13×C19C32
FrattiniC1G
Fitting, socleC22×C3×C13×C19C3
LCSG ▷ C22×C13×C19
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

996 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 284);