Finite Group Databasebeta

C22×C4×#6131 #16769494

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

Aliases

direct productC22×C4×#6131

Splittings

FittingC22×C4×Q8×C13 ⋊ C2
SylowC13 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC2×C13C25×C4
FrattiniC22C25×D13
FittingC22×C4×Q8×C13C2
socleC24×C13C24
prime radicalC23×#6131C2
cosocleC22×C13C26
hypercenterC22×C4×Q8D13
hypocenterC13C22×C4×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

12878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076143);