Finite Group Databasebeta

C4×C22⋊D997 #44542262

order31904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D997

Splittings

FittingC22×C4×C997 ⋊ C2
SylowC997 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D997
commutatorC2×C997C22×C4
FrattiniC22C22×D997
FittingC22×C4×C997C2
socle, cosocleC22×C997C23
prime radicalC2×C22⋊D997C2
hypercenterC22×C4D997
hypocenterC997C4×D4
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C2×C4 ◁ C22×C4

94 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, 107);