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C22⋊C4×C22⋊D163 #35217355

order20864
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×C22⋊D163

Splittings

FittingC22×C22⋊C4×C163 ⋊ C2
SylowC163 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D163
commutatorC22×C163C23×C4
FittingC22×C22⋊C4×C163C2
socle, cosocleC23×C163C24
prime radicalC23×C22⋊D163C2
hypercenterC22×C22⋊C4D163
hypocenterC163D4×C22⋊C4
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5216

Conjugacy classes & character table

3290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 7329);