Finite Group Databasebeta

C2×2−1+4×Dic13 #16769529

order3328
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×Dic13

Splittings

SylowC13 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC23C24×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
Fitting, prime radicalC22×C13×2−1+4C2
socleC23×C13C25
cosocleC22×C13C26
hypercenterC22×2−1+4D13
hypocenterC13C2×C4×2−1+4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076178);