Finite Group Databasebeta

#137×C47⋊C8 #26185705

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

Aliases

direct product#137×C47⋊C8

Splittings

SylowC47 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC4×#137×C47C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×C47C2×C4
cosocleC42×C47C24
hypercenterC4×#137D47
hypocenterC47C8×#137
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

714 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138995);