Finite Group Databasebeta

C22×Dic1934 #44526161

order30944
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1934

Splittings

SylowC967 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D967
commutator, cosocleC2×C967C24
FrattiniC2C23×D967
FittingC22×C4×C967C2
socle, prime radicalC23×C967C22
hypercenterC22×C4D967
hypocenterC967C22×Q8
LCSG ▷ C2×C967 ▷ C967
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30944

Conjugacy classes & character table

7748 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 186);