Finite Group Databasebeta

C4×#15689293 #26222156

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#15689293

Splittings

FittingC4×#100×C47 ⋊ C2
SylowC47 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2×C4#13093994
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#100×C47C2
socleC22×C47C2×#120
prime radicalC2×#15689293C2
cosocleC22×C4×C47C24
hypercenterC4×#100D47
hypocenterC47C4×#453
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

1578 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 175446);