Finite Group Databasebeta

C2×#28417885 #44470068

order29888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28417885

Splittings

SylowC467 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23D1868
commutatorC4×C467C22×C4
FrattiniC2×C4C22×D467
FittingC22×C8×C467C2
socle, prime radicalC23×C467D4
cosocleC2×C4×C467C23
hypercenterC22×C8D467
hypocenterC467C2×#106
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Conjugacy classes & character table

7484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 580);