Finite Group Databasebeta

C2×#20243399 #26215732

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243399

Splittings

FittingC22×C4⋊C8×C47 ⋊ C2
SylowC47 ⋊ C2×#1804

Subgroups

subgroupG/H
centerC24C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C4⋊C8×C47C2
socleC24×C47C2×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenterC22×C4⋊C8D47
hypocenterC47C2×#1804
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

1942 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, 169022);