Finite Group Databasebeta

#107×D188 #26234397

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#107×D188

Splittings

FittingC4×#107×C47 ⋊ C2
SylowC47 ⋊ D4×#107

Subgroups

subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#107×C47C2
socleC23×C47C22×D4
prime radicalC22×D188D4
cosocleC22×C4×C47C24
hypercenterC4×#107D47
hypocenterC47D4×#107
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#107

1126 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, 187687);