Finite Group Databasebeta

C2×#20243731 #26217612

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

Aliases

direct productC2×#20243731

Splittings

SylowC47 ⋊ C2×#1878

Subgroups

subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC23×Q16×C47C2
socle, prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC23×Q16D47
hypocenterC47C2×#1878
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q16

1822 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170902);