Finite Group Databasebeta

C2×#20242108 #26184801

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

Aliases

direct productC2×#20242108

Splittings

FittingC2×C47×#423 ⋊ C2
SylowC47 ⋊ C2×#1557

Subgroups

subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#423C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689673C2
cosocleC42×C47C24
hypercenterC2×#423D47
hypocenterC47C2×#1557
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

1278 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138091);