Finite Group Databasebeta

C4×D3688 #44442160

order29504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×D3688

Splittings

FittingC4×C8×C461 ⋊ C2
SylowC461 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2×C4D1844
commutatorC4×C461C22×C4
FrattiniC2×C4C22×D461
FittingC4×C8×C461C2
socleC22×C461C2×D4
prime radicalC2×D3688C2
cosocleC2×C4×C461C23
hypercenterC4×C8D461
hypocenterC461C4×D8
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

7388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 633);