Finite Group Databasebeta

C4×#11718266 #16785241

order3328
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#11718266

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C4×#344

Subgroups

subgroupG/H
centerC42C22⋊#261
commutatorC22×C13C43
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC22×C13C2×#95
prime radicalC23×D13C22×C4
cosocleC22×C4×D13C23
hypercenterC2×C4×C8#261
hypocenterC13C4×#344
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1091890);