Finite Group Databasebeta

C22×#21418726 #44470796

order29888
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#21418726

Splittings

FittingC22×C8×C467 ⋊ C2
SylowC467 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D467
commutatorC2×C467C23×C4
FrattiniC4C23×D467
FittingC22×C8×C467C2
socleC23×C467C2×C4
prime radicalC23×D467C4
cosocleC4×C467C24
hypercenterC22×C8D467
hypocenterC467C22×M16
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C22×C4 ◁ C22×C8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

7496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1308);