Finite Group Databasebeta

C2×C8×#10625337 #26185647

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×#10625337

Splittings

SylowC47 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC22×C8C22⋊D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC2×C8×Q8×C47C2
socle, prime radicalC23×C47C4×D4
cosocleC42×C47C24
hypercenterC2×C8×Q8D47
hypocenterC47C2×C8×Q16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C8×Q8

734 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138937);