Finite Group Databasebeta

C8×#10587616 #17040352

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×#10587616

Splittings

FittingC22×C4×C8×C17 ⋊ C2
SylowC17 ⋊ C8×#121

Subgroups

subgroupG/H
centerC22×C8C22×D17
commutatorC22×C17C23×C8
FrattiniC22×C4C23×D17
FittingC22×C4×C8×C17C2
socleC23×C17C23×C4
prime radicalC2×#10587616C4
cosocleC22×C4×C17C24
hypercenterC22×C4×C8D17
hypocenterC17C8×#121
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 175596);