Finite Group Databasebeta

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C4×#15689604 #26374522

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#15689604

Splittings

FittingC2×C4×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C4×#520

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C4×C4⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×#10625350C22
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C4×#520
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

3698 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327812);