Finite Group Databasebeta

C4×#15689295 #26222172

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

Aliases

direct productC4×#15689295

Splittings

FittingC4×#124×C47 ⋊ C2
SylowC47 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#124×C47C2
socleC22×C47C2×#120
prime radicalC2×#15689295C2
cosocleC22×C4×C47C24
hypercenterC4×#124D47
hypocenterC47C4×#454
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#124

1390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 175462);