Finite Group Databasebeta

C4×#21418726 #44469987

order29888
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#21418726

Splittings

FittingC4×C8×C467 ⋊ C2
SylowC467 ⋊ C4×M16

Subgroups

subgroupG/H
centerC42C2×D467
commutatorC2×C467C2×C42
FrattiniC2×C4C22×D467
FittingC4×C8×C467C2
socleC22×C467C22×C4
prime radicalC22×D467C2×C4
cosocleC2×C4×C467C23
hypercenterC4×C8D467
hypocenterC467C4×M16
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C42 ◁ C4×C8

142 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, 499);