Finite Group Databasebeta

C4×#11762541 #16924922

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#11762541

Splittings

SylowC17 ⋊ C4×Q8⋊C8

Subgroups

subgroupG/H
centerC2×C42D68
commutatorC4×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC42×C8×C17C2
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenterC42×C8D17
hypocenterC17C4×Q8⋊C8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60166);