Finite Group Databasebeta

C8×#88201 #15870786

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#88201

Splittings

FittingC2×C8×Q8×C13 ⋊ C2
SylowC13 ⋊ C8×#124

Subgroups

subgroupG/H
centerC22×C8C22×D13
commutatorC22×C13C23×C8
FrattiniC22×C4C23×D13
FittingC2×C8×Q8×C13C2
socleC23×C13C23×C4
prime radicalC22×D52C2×C4
cosocleC22×C4×C13C24
hypercenterC2×C8×Q8D13
hypocenterC13C8×#124
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 177435);