Finite Group Databasebeta

C8×#10587587 #16999909

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#10587587

Splittings

FittingC2×C82×C17 ⋊ C2
SylowC17 ⋊ C8×#131

Subgroups

subgroupG/H
centerC82C2×D17
commutatorC2×C17C22×C4×C8
FrattiniC42C23×D17
FittingC2×C82×C17C2
socleC22×C17C22×C42
prime radicalC2×#63252C2×C4
cosocleC42×C17C24
hypercenterC2×C82D17
hypocenterC17C8×#131
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C82 ◁ C2×C82

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135153);