Finite Group Databasebeta

C2×C4×(C2×#595)⋊C4 #17962909

order4352
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×C4×(C2×#595)⋊C4

Splittings

FittingC22×C42×C17 ⋊ C4
SylowC17 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C2×C43
FrattiniC23C23×#595
FittingC22×C42×C17C4
socleC24×C17C22×C4
prime radicalC24×D17C23
cosocleC23×D17C24
hypercenterC22×C42#595
hypocenterC17C2×C4×#95
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42

4462 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, 1098153);