Finite Group Databasebeta

C8×Dic878 #43243729

order28096
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic878

Splittings

SylowC439 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D439
commutatorC2×C439C22×C8
FrattiniC2×C4C22×D439
FittingC4×C8×C439C2
socle, prime radicalC22×C439C22×C4
cosocleC2×C4×C439C23
hypercenterC4×C8D439
hypocenterC439C8×Q8
LCSG ▷ C2×C439 ▷ C439
UCSC1 ◁ C2×C8 ◁ C4×C8

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28096

Conjugacy classes & character table

7048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 674);