Finite Group Databasebeta

C4×#11719475 #16727144

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#11719475

Splittings

FittingC4×C13×#135 ⋊ C2
SylowC13 ⋊ C4×#577

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC4×C13×#135C2
socleC22×C13C23×D4
prime radicalC2×#11719475C2
cosocleC2×C4×C13C25
hypercenterC4×#135D13
hypocenterC13C4×#577
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#135

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033793);