Finite Group Databasebeta

C8×#6292 #13159606

order1728
isoclinismisoclinic class of #6290
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3

Aliases

direct productC8×#6292

Splittings

SylowC33 ⋊ C8×D4

Subgroups

subgroupG/H
center, hypercenterC2×C8D3×C3⋊D3
commutatorC2×C33C22×C8
FrattiniC2×C4C2×D3×C3⋊D3
FittingC2×C33×C8C22
socleC22×C33C22×C4
prime radicalC2×#6292C4
cosocleC2×C33×C4C23
hypocenterC33C8×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C8

1108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 25669);