Finite Group Databasebeta

C2×C4⋊Dic809 #39905754

order25888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊Dic809

Splittings

SylowC809 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D809
commutatorC2×C809C22×C4
FrattiniC22C22×D809
FittingC22×C4×C809C2
socle, prime radicalC23×C809C22
cosocleC22×C809C23
hypercenterC22×C4D809
hypocenterC809C2×C4⋊C4
LCSG ▷ C2×C809 ▷ C809
UCSC1 ◁ C23 ◁ C22×C4

92 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, 101);