Finite Group Databasebeta

C22×Dic1994 #44542341

order31904
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1994

Splittings

SylowC997 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D997
commutator, cosocleC2×C997C24
FrattiniC2C23×D997
FittingC22×C4×C997C2
socle, prime radicalC23×C997C22
hypercenterC22×C4D997
hypocenterC997C22×Q8
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31904

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, 186);