Finite Group Databasebeta

C2×#20243729 #26217610

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

Aliases

direct productC2×#20243729

Splittings

SylowC47 ⋊ C2×#1878

Subgroups

subgroupG/H
centerC24C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C4×Q8×C47C2
socle, prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC22×C4×Q8D47
hypocenterC47C2×#1878
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×Q8

1822 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, 170900);