Finite Group Databasebeta

C8×#13093993 #26221773

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC8×#13093993

Splittings

FittingC24×C8×C47 ⋊ C2
SylowC47 ⋊ C8×#120

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC24×C8×C47C2
socleC23×C47C23×C4
prime radicalC2×#13093993C4
cosocleC22×C4×C47C24
hypercenterC24×C8D47
hypocenterC47C8×#120
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C24×C8

1786 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 175063);