Finite Group Databasebeta

C8×#16813884 #44408691

order29056
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#16813884

Splittings

FittingC2×C4×C8×C227 ⋊ C2
SylowC227 ⋊ C8×#41

Subgroups

subgroupG/H
centerC4×C8C2×D227
commutatorC2×C227C23×C8
FrattiniC2×C4C23×D227
FittingC2×C4×C8×C227C2
socleC22×C227C23×C4
prime radicalC2×#16813884C4
cosocleC2×C4×C227C24
hypercenterC2×C4×C8D227
hypocenterC227C8×#41
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13467);