Finite Group Databasebeta

C2×C4×Dic778 #38734564

order24896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic778

Splittings

SylowC389 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D389
commutatorC2×C389C23×C4
FrattiniC22C23×D389
FittingC2×C42×C389C2
socle, prime radicalC23×C389C23
cosocleC22×C389C24
hypercenterC2×C42D389
hypocenterC389C2×C4×Q8
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22×C4 ◁ C2×C42

298 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, 1014);