Finite Group Databasebeta

C3×#10587480 #13108752

order1632
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10587480

Splittings

FittingC3×C4⋊C4×C17 ⋊ C2
HallC3×C17 ⋊ #102
SylowC17 ⋊ C3×#102

Subgroups

subgroupG/H
centerC22×C3C22⋊D17
commutatorC4×C17C2×C3×C4
FrattiniC2×C4C2×C3×D17
FittingC3×C4⋊C4×C17C2
socleC22×C3×C17D4
prime radicalC2×C3×D68C2
cosocleC2×C4×C17C22×C3
hypercenterC3×C4⋊C4D17
hypocenterC17C3×#102
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1632, 87);