Finite Group Databasebeta

C2×#20241840 #26182875

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

Aliases

direct productC2×#20241840

Splittings

FittingC22×C4×C8×C47 ⋊ C2
SylowC47 ⋊ C2×#1492

Subgroups

subgroupG/H
centerC22×C4C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC22×C4×C8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689673C2
cosocleC42×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C2×#1492
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 136165);