Finite Group Databasebeta

C22×#16836582 #28417208

order14912
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16836582

Splittings

SylowC233 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D233
commutator, cosocleC4×C233C24
FrattiniC4C23×D233
Fitting, prime radicalC22×D4×C233C2
socleC23×C233D4
hypercenterC22×D4D233
hypocenterC233C22×SD16
LCSG ▷ C4×C233 ▷ C2×C233 ▷ C233
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1322);