Finite Group Databasebeta

Q8×#10587587 #17898735

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#10587587

Splittings

FittingC2×C8×Q8×C17 ⋊ C2
SylowC17 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D17
commutator, socleC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C8×Q8×C17C2
prime radicalC2×#63252C23
cosocleC2×C4×C17C25
hypercenterC2×C8×Q8D17
hypocenterC17Q8×#131
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×C8×Q8

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033979);