Finite Group Databasebeta

C4×D8×D227 #44408481

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×D8×D227

Splittings

FittingC4×D8×C227 ⋊ C2
SylowC227 ⋊ C2×C4×D8

Subgroups

subgroupG/H
centerC2×C4D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC4×D8×C227C2
socleC22×C227C22×D4
prime radicalC2×D8×D227C2
cosocleC2×C4×C227C24
hypercenterC4×D8D227
hypocenterC227C2×C4×D8
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13257);