Finite Group Databasebeta

C2×C8×C22⋊D137 #31789460

order17536
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×C22⋊D137

Splittings

FittingC23×C8×C137 ⋊ C2
SylowC137 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C8C2×D137
commutatorC2×C137C23×C8
FrattiniC2×C4C23×D137
FittingC23×C8×C137C2
socleC23×C137C22×C4
prime radicalC22×C22⋊D137C4
cosocleC2×C4×C137C24
hypercenterC23×C8D137
hypocenterC137C2×C8×D4
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C22×C8 ◁ C23×C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8768

Conjugacy classes & character table

4432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 13181);