Finite Group Databasebeta

C22×#15688862 #26184153

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

Aliases

direct productC22×#15688862

Splittings

FittingC22×#97×C47 ⋊ C2
SylowC47 ⋊ C22×#329

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC22×#97×C47C2
socleC24×C47C22⋊C4
prime radicalC23×D188C4
cosocleC42×C47C24
hypercenterC22×#97D47
hypocenterC47C22×#329
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

1502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 137443);