Finite Group Databasebeta

C2×#20241498 #26131202

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241498

Splittings

SylowC47 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#13093944
commutatorC8×C47C2×C42
FrattiniC22×C8C22×D47
FittingC22×#108×C47C2
socleC23×C47#102
prime radicalC24×C47SD16
cosocleC22×C8×C47C23
hypercenterC22×#108D47
hypocenterC47C2×#1387
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

614 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, 84492);