Finite Group Databasebeta

Q8×#10587488 #17053151

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

Aliases

direct productQ8×#10587488

Splittings

SylowC17 ⋊ Q8×#106

Subgroups

subgroupG/H
centerC23C22×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C8×Q8×C17C2
socle, prime radicalC23×C17C22×D4
cosocleC22×C4×C17C24
hypercenterC2×C8×Q8D17
hypocenterC17Q8×#106
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 188395);