Finite Group Databasebeta

C3×C22⋊#3622 #13108773

order1632
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×C22⋊#3622

Splittings

HallC3×C17 ⋊ C22⋊C8
SylowC17 ⋊ C3×C22⋊C8

Subgroups

subgroupG/H
centerC2×C3×C4C2×D17
commutatorC2×C17C2×C3×C8
FrattiniC2×C4C2×C3×D17
FittingC22×C3×C4×C17C2
socleC22×C3×C17C2×C4
prime radicalC23×C3×C17C4
cosocleC2×C4×C17C22×C3
hypercenterC22×C3×C4D17
hypocenterC17C3×C22⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 108);