Finite Group Databasebeta

C22⋊C4×D997 #44542251

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

Aliases

direct productC22⋊C4×D997

Splittings

FittingC22⋊C4×C997 ⋊ C2
SylowC997 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D997
commutatorC2×C997C22×C4
FittingC22⋊C4×C997C2
socle, cosocleC22×C997C23
prime radicalC23×D997C2
hypercenterC22⋊C4D997
hypocenterC997C2×C22⋊C4
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7976

Conjugacy classes & character table

5000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31904, 96);