Finite Group Databasebeta

C23×D4×#595 #17981033

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×D4×#595
unambiguous semidirect productD17⋊(C22×C4×D4)

Splittings

FittingC23×D4×C17 ⋊ C4
SylowC17 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC2×C17C25×C4
FrattiniC2C25×#595
FittingC23×D4×C17C4
socleC24×C17C22×C4
prime radicalC23×D4×D17C2
cosocleC2×D17C26
hypercenterC23×D4#595
hypocenterC17C23×C4×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×D4

19998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1116277);