Finite Group Databasebeta

C22×#21418730 #44470809

order29888
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#21418730

Splittings

FittingC22×Q8×C467 ⋊ C2
SylowC467 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D467
commutator, cosocleC4×C467C24
FrattiniC4C23×D467
FittingC22×Q8×C467C2
socleC23×C467D4
prime radicalC22×D1868C2
hypercenterC22×Q8D467
hypocenterC467C22×SD16
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

4688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1321);