Finite Group Databasebeta

#108×D188 #26234532

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

Aliases

direct product#108×D188

Splittings

FittingC4×#108×C47 ⋊ C2
SylowC47 ⋊ D4×#108

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#108×C47C2
socleC22×C47C22×C4⋊C4
prime radicalC22×D188Q8
cosocleC22×C4×C47C24
hypercenterC4×#108D47
hypocenterC47D4×#108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

894 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 187822);