Finite Group Databasebeta

C4×#11762622 #16949577

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11762622

Splittings

SylowC17 ⋊ C4×#361

Subgroups

subgroupG/H
centerC2×C4#10587503
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC2×C4×D8×C17C2
socleC22×C17C2×#102
prime radicalC22×D8×C17C22
cosocleC22×C8×C17C23
hypercenterC2×C4×D8D17
hypocenterC17C4×#361
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

498 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, 84821);