Finite Group Databasebeta

C8×Q8×#595 #17968852

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

Aliases

direct productC8×Q8×#595

Splittings

FittingC8×Q8×C17 ⋊ C4
SylowC17 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC2×C8C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC2×C4C23×#595
FittingC8×Q8×C17C4
socleC22×C17C22×C42
prime radicalC22×D17C23×C4
cosocleC2×C4×D17C24
hypercenterC8×Q8#595
hypocenterC17C4×C8×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C8×Q8

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104096);