Finite Group Databasebeta

C2×#20244299 #26220273

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20244299

Splittings

SylowC47 ⋊ C2×#1978

Subgroups

subgroupG/H
centerC23#13093995
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC23×D8×C47C2
socleC23×C47#121
cosocleC22×C4×C47C24
hypercenterC23×D8D47
hypocenterC47C2×#1978
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1694 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, 173563);