Finite Group Databasebeta

C4×D3736 #44470121

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

Aliases

direct productC4×D3736

Splittings

FittingC4×C8×C467 ⋊ C2
SylowC467 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2×C4D1868
commutatorC4×C467C22×C4
FrattiniC2×C4C22×D467
FittingC4×C8×C467C2
socleC22×C467C2×D4
prime radicalC2×D3736C2
cosocleC2×C4×C467C23
hypercenterC4×C8D467
hypocenterC467C4×D8
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

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, 633);