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C4⋊C4×D1087 #46852141

order34784
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D1087

Splittings

FittingC4⋊C4×C1087 ⋊ C2
SylowC1087 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D1087
commutatorC2×C1087C22×C4
FittingC4⋊C4×C1087C2
socle, cosocleC22×C1087C23
prime radicalC22×D1087C22
hypercenterC4⋊C4D1087
hypocenterC1087C2×C4⋊C4
LCSG ▷ C2×C1087 ▷ C1087
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17392

Conjugacy classes & character table

5450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34784, 99);