Finite Group Databasebeta

C22×#19154562 #37554955

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

Aliases

direct productC22×#19154562

Splittings

FittingC22×D4×C367 ⋊ C2
SylowC367 ⋊ C22×D8

Subgroups

subgroupG/H
centerC23C22⋊D367
commutator, cosocleC4×C367C24
FrattiniC4C23×D367
FittingC22×D4×C367C2
socleC23×C367D4
hypercenterC22×D4D367
hypocenterC367C22×D8
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

3688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1318);