Finite Group Databasebeta

C2×#30630112 #44542306

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

Aliases

direct productC2×#30630112

Splittings

SylowC997 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D997
commutatorC2×C997C22×C4
FrattiniC4C22×D997
FittingC22×C4×C997C2
socleC22×C997C2×C4
prime radicalC23×C997C4
cosocleC4×C997C23
hypercenterC22×C4D997
hypocenterC997C2×M16
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C2×C4 ◁ C22×C4

68 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, 151);