Finite Group Databasebeta

C4×#11718062 #15753796

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11718062

Splittings

FittingC4×C13×C22⋊C8 ⋊ C2
SylowC13 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22×C4#6103
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC4×C13×C22⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC4×C22⋊C8D13
hypocenterC13C4×#327
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 60445);