Finite Group Databasebeta

C2×#20245307 #26370028

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245307

Splittings

FittingC2×C47×C22⋊C16 ⋊ C2
SylowC47 ⋊ C2×#2185

Subgroups

subgroupG/H
centerC23C2×D376
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×C22⋊C16C2
socleC23×C47C2×D8
prime radicalC2×#15689359C2
hypercenterC2×C22⋊C16D47
hypocenterC47C2×#2185
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

1178 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1898 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323318);