Finite Group Databasebeta

C2×D4×D13⋊C8 #16808247

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC2×D4×D13⋊C8
unambiguous semidirect productD13⋊(C2×C8×D4)

Splittings

SylowC13 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C24×C8
FrattiniC22C24×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C4
cosocleC2×Dic13C25
hypercenterC2×C4×D4#261
hypocenterC13C22×C8×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114896);