Finite Group Databasebeta

C2×C13×C4⋊Dic3 #11928901

order1248
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23

Aliases

direct productC2×C13×C4⋊Dic3

Splittings

HallC3×C13 ⋊ C2×C4⋊C4
SylowC3 ⋊ C2×C13×C4⋊C4

Subgroups

subgroupG/H
centerC23×C13C2×D3
commutatorC2×C3C22×C4×C13
FrattiniC22C22×D3×C13
FittingC22×C3×C4×C13C2
socle, prime radicalC23×C3×C13C22
cosocleC22×C3C23×C13
hypercenterC22×C4×C13D3
hypocenterC3C2×C13×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C13 ◁ C22×C4×C13

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1248

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1013);