Finite Group Databasebeta

C2×Q8×C22⋊#595 #17978967

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×Q8×C22⋊#595
unambiguous semidirect productD17⋊(Q8×C22⋊C4)

Splittings

FittingC23×Q8×C17 ⋊ C4
SylowC17 ⋊ C2×Q8×C22⋊C4

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC23×Q8×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC23×Q8#595
hypocenterC17C2×Q8×C22⋊C4
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×Q8

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114211);