Finite Group Databasebeta

C22×D2936 #37554956

order23488
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×D2936

Splittings

FittingC22×C8×C367 ⋊ C2
SylowC367 ⋊ C22×D8

Subgroups

subgroupG/H
centerC23D1468
commutator, cosocleC4×C367C24
FrattiniC4C23×D367
FittingC22×C8×C367C2
socleC23×C367D4
hypercenterC22×C8D367
hypocenterC367C22×D8
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

5884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1319);