Finite Group Databasebeta

C23×(C2×#595)⋊C4 #17978846

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C212

Aliases

direct productC23×(C2×#595)⋊C4
unambiguous semidirect productD17⋊(C22×#95)

Splittings

FittingC24×C4×C17 ⋊ C4
SylowC17 ⋊ C23×#95

Subgroups

subgroupG/H
centerC25C2×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC24×C4×C17C4
socleC25×C17C2×C4
prime radicalC25×D17C22
cosocleC22×D17C25
hypercenterC24×C4#595
hypocenterC17C23×#95
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C25 ◁ C24×C4

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1114090);