Finite Group Databasebeta

#41×C22⋊Dic47 #26375483

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#41×C22⋊Dic47

Splittings

SylowC47 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
Fitting, prime radicalC23×#41×C47C2
socle, cosocleC23×C47C25
hypercenterC23×#41D47
hypocenterC47C22⋊C4×#41
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328773);