Finite Group Databasebeta

C4×#11762536 #16924919

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11762536

Splittings

FittingC4×C17×C4⋊C8 ⋊ C2
SylowC17 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D17
commutatorC4×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC4×C17×C4⋊C8C2
socleC23×C17C2×C22⋊C4
prime radicalC22×D68C2×C4
cosocleC2×C42×C17C23
hypercenterC4×C4⋊C8D17
hypocenterC17C4×D4⋊C8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60163);