Finite Group Databasebeta

C4×#11718808 #16016237

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11718808

Splittings

FittingC2×C4×C13×D8 ⋊ C2
SylowC13 ⋊ C4×#509

Subgroups

subgroupG/H
centerC2×C4C2×#6104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C4×C13×D8C2
socleC22×C13C22×D8
prime radicalC2×#11718808C2
cosocleC2×C8×C13C24
hypercenterC2×C4×D8D13
hypocenterC13C4×#509
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322886);