Finite Group Databasebeta

C2×C8×#63242 #17963967

order4352
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C22×C82 · Schur multiplier (H2) = C25×C8

Aliases

direct productC2×C8×#63242

Splittings

derived, SylowC17 ⋊ C22×C82

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8#595
commutator, hypocenterC17C22×C82
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC23×C17C2×C42
prime radicalC23×D17C42
cosocleC4×Dic17C24
LCSG ▷ C17
UCSC1 ◁ C2×C4×C8

1342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1099211);