Finite Group Databasebeta

C2×#20242154 #26185295

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20242154

Splittings

FittingC2×C47×#335 ⋊ C2
SylowC47 ⋊ C2×#1569

Subgroups

subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#335C2
socleC23×C47C2×C4⋊C4
prime radicalC23×D47C4⋊C4
cosocleC42×C47C24
hypercenterC2×#335D47
hypocenterC47C2×#1569
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

758 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138585);