Finite Group Databasebeta

C8×C22⋊#3624 #17951720

order4352
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×C22⋊#3624

Splittings

SylowC17 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC22×C8C2×#595
commutatorC2×C17C2×C82
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC23×C17C2×C42
prime radicalC24×C17C42
cosocleC2×C4×Dic17C23
hypercenterC23×C8#595
hypocenterC17C8×C22⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C23×C8

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1086964);