Finite Group Databasebeta

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C4×#15688885 #26121458

order12032
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#15688885

Splittings

SylowC47 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23×C4C22⋊D47
commutatorC4×C47C43
FrattiniC23×C4C22×D47
FittingC2×C4×C4⋊C4×C47C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C4×#340
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1182 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 74748);