Finite Group Databasebeta

Q8×#10587476 #17051024

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#10587476

Splittings

FittingC42×Q8×C17 ⋊ C2
SylowC17 ⋊ Q8×#104

Subgroups

subgroupG/H
centerC2×C4C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC42×Q8×C17C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#63252C23
cosocleC22×C4×C17C24
hypercenterC42×Q8D17
hypocenterC17Q8×#104
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C42×Q8

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 186268);