Finite Group Databasebeta

#364×Dic47 #26131598

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct product#364×Dic47

Splittings

SylowC47 ⋊ C4×#364

Subgroups

subgroupG/H
centerC2×C8D4×D47
commutatorC4×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#364C2
socleC22×C47C2×C4⋊C8
prime radicalC23×C47C2×M16
cosocleC22×C8×C47C23
hypercenterC2×#364D47
hypocenterC47C4×#364
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#364

398 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 84888);