Finite Group Databasebeta

C4×#11718086 #15778306

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

Aliases

direct productC4×#11718086

Splittings

SylowC13 ⋊ C4×#365

Subgroups

subgroupG/H
centerC2×C4#88048
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC4×C13×#108C2
socleC22×C13C2×#106
prime radicalC23×C13C2×SD16
cosocleC22×C8×C13C23
hypercenterC4×#108D13
hypocenterC13C4×#365
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#108

330 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, 84955);