Finite Group Databasebeta

#102×C22⋊D13 #15878321

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#102×C22⋊D13

Splittings

FittingC22×C13×#102 ⋊ C2
SylowC13 ⋊ D4×#102

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#102C2
socleC23×C13C22×D4
prime radicalC2×D4×C22⋊D13C2
cosocleC22×C4×C13C24
hypercenterC22×#102D13
hypocenterC13D4×#102
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

2014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 184970);