Finite Group Databasebeta

C2×C4×Dic958 #44500860

order30656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic958

Splittings

SylowC479 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D479
commutatorC2×C479C23×C4
FrattiniC22C23×D479
FittingC2×C42×C479C2
socle, prime radicalC23×C479C23
cosocleC22×C479C24
hypercenterC2×C42D479
hypocenterC479C2×C4×Q8
LCSG ▷ C2×C479 ▷ C479
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30656

Conjugacy classes & character table

7688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 1014);