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C2×C4×C4⋊C4×D47 #26374454

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×C4⋊C4×D47

Splittings

FittingC2×C4×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C4×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C22×C4×C4⋊C4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

5758 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, 327744);