Finite Group Databasebeta

C4×#11718364 #15871001

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11718364

Splittings

SylowC13 ⋊ C4×#491

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#97C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC4×#97D13
hypocenterC13C4×#491
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 177650);