Finite Group Databasebeta

C2×C4×Q8×#595 #17978855

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×Q8×#595
unambiguous semidirect productD17⋊(C42×Q8)

Splittings

FittingC2×C4×Q8×C17 ⋊ C4
SylowC17 ⋊ C2×C42×Q8

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC2×C4×Q8×C17C4
socleC23×C17C23×C4
prime radicalC23×D17C24
cosocleC22×D17C25
hypercenterC2×C4×Q8#595
hypocenterC17C2×C42×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

3966 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, 1114099);