Finite Group Databasebeta

C4×#11718410 #15869797

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

Aliases

direct productC4×#11718410

Splittings

FittingC4×C13×#100 ⋊ C2
SylowC13 ⋊ C4×#472

Subgroups

subgroupG/H
centerC2×C4#88138
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#100C2
socleC22×C13C2×#121
prime radicalC2×#11718410C2
cosocleC22×C4×C13C24
hypercenterC4×#100D13
hypocenterC13C4×#472
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 176446);