Finite Group Databasebeta

C22×C8×#67 #11659017

order768
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×C8×#67

Splittings

FittingC24×C3×C8 ⋊ C2
SylowC3 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC23×C8C2×D3
commutatorC2×C3C24×C8
FrattiniC2×C4C24×D3
FittingC24×C3×C8C2
socleC24×C3C22×C4
prime radicalC23×#67C4
cosocleC2×C3×C4C25
hypercenterC24×C8D3
hypocenterC3C22×C8×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C8 ◁ C24×C8

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1033398);