Finite Group Databasebeta

C2×C4×C8×#595 #17968120

order4352
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C2×C42×C8 · Schur multiplier (H2) = C23×C43

Aliases

direct productC2×C4×C8×#595

Splittings

FittingC2×C4×C8×C17 ⋊ C4
derived, SylowC17 ⋊ C2×C42×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8#595
commutator, hypocenterC17C2×C42×C8
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC23×C17C2×C42
prime radicalC23×D17C22×C4
cosocleC2×C4×D17C24
LCSG ▷ C17
UCSC1 ◁ C2×C4×C8

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1103364);