Finite Group Databasebeta

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C4⋊C4×#10625354 #26375594

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4⋊C4×#10625354

Splittings

FittingQ8×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C4⋊C4×#41

Subgroups

subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingQ8×C4⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×#10625354C22
hypercenterQ8×C4⋊C4D47
hypocenterC47C4⋊C4×#41
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3250 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328884);