Finite Group Databasebeta

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C4×C4⋊C4×Dic47 #26137356

order12032
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC4×C4⋊C4×Dic47

Splittings

SylowC47 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC2×C47C2×C43
FrattiniC24C23×D47
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C42×C4⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2478 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90646);