Finite Group Databasebeta

C2×C22⋊Dic997 #44542253

order31904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic997

Splittings

SylowC997 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D997
commutatorC2×C997C22×C4
FrattiniC22C22×D997
Fitting, prime radicalC24×C997C2
socleC23×C997C22
cosocleC22×C997C23
hypercenterC24D997
hypocenterC997C2×C22⋊C4
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15952

Conjugacy classes & character table

7988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31904, 98);