Finite Group Databasebeta

C22×(C2×#595)⋊Q8 #17978888

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×(C2×#595)⋊Q8
unambiguous semidirect productD17⋊(C2×#391)

Splittings

FittingC23×Q8×C17 ⋊ C4
SylowC17 ⋊ C22×#391

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC23×Q8×C17C4
socleC24×C17C22×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC23×Q8#595
hypocenterC17C22×#391
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×Q8

6174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114132);