Finite Group Databasebeta

C2×#28417892 #44470451

order29888
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28417892

Splittings

FittingC2×C16×C467 ⋊ C2
SylowC467 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D467
commutatorC2×C467C22×C8
FrattiniC8C22×D467
FittingC2×C16×C467C2
socleC22×C467C2×C8
prime radicalC22×D467C8
cosocleC8×C467C23
hypercenterC2×C16D467
hypocenterC467C2×M32
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C8 ◁ C2×C16

90 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, 963);