Finite Group Databasebeta

C8×Dic778 #38734224

order24896
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC8×Dic778

Splittings

SylowC389 ⋊ C8×Q8

Subgroups

subgroupG/H
centerC2×C8C2×D389
commutatorC2×C389C22×C8
FrattiniC2×C4C22×D389
FittingC4×C8×C389C2
socle, prime radicalC22×C389C22×C4
cosocleC2×C4×C389C23
hypercenterC4×C8D389
hypocenterC389C8×Q8
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C2×C8 ◁ C4×C8

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

6248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 674);