Finite Group Databasebeta

C4×Dic1618 #39905765

order25888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic1618

Splittings

SylowC809 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D809
commutatorC2×C809C22×C4
FrattiniC22C22×D809
FittingC42×C809C2
socle, prime radical, cosocleC22×C809C23
hypercenterC42D809
hypocenterC809C4×Q8
LCSG ▷ C2×C809 ▷ C809
UCSC1 ◁ C2×C4 ◁ C42

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25888

Conjugacy classes & character table

6484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25888, 112);