Finite Group Databasebeta

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C4×#15689418 #26223873

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#15689418

Splittings

SylowC47 ⋊ C4×#477

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC42×Q8×C47C2
socle, prime radicalC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC42×Q8D47
hypocenterC47C4×#477
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×Q8

880 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 177163);