Finite Group Databasebeta

C2×D4×C251⋊C8 #44559038

order32128
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×C251⋊C8

Splittings

SylowC251 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D251
commutatorC2×C251C23×C8
FrattiniC2×C4C23×D251
FittingC2×C4×D4×C251C2
socleC23×C251C22×C4
prime radicalC22×D4×C251C4
cosocleC2×C4×C251C24
hypercenterC2×C4×D4D251
hypocenterC251C2×C8×D4
LCSG ▷ C2×C251 ▷ C251
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16064

Conjugacy classes & character table

5080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32128, 13183);