Finite Group Databasebeta

← Prev (#26234672) Next (#26234674) →

C4⋊C4×D376 #26234673

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

Aliases

direct productC4⋊C4×D376

Splittings

FittingC8×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C4⋊C4×D8

Subgroups

subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC8×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC22×D376C22
cosocleC22×C4×C47C24
hypercenterC8×C4⋊C4D47
hypocenterC47C4⋊C4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

1134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 187963);