Finite Group Databasebeta

C2×Dic983⋊C4 #44537917

order31456
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×Dic983⋊C4

Splittings

SylowC983 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D983
commutatorC2×C983C22×C4
FrattiniC22C22×D983
FittingC22×C4×C983C2
socle, prime radicalC23×C983C22
cosocleC22×C983C23
hypercenterC22×C4D983
hypocenterC983C2×C4⋊C4
LCSG ▷ C2×C983 ▷ C983
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31456

Conjugacy classes & character table

7876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 100);