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C4×(C22⋊D163)⋊C4 #35216880

order20864
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×(C22⋊D163)⋊C4

Splittings

FittingC4×C22⋊C4×C163 ⋊ C2
SylowC163 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D163
commutatorC2×C163C22×C42
FrattiniC23C23×D163
FittingC4×C22⋊C4×C163C2
socle, cosocleC23×C163C24
prime radicalC22×C22⋊D163C22
hypercenterC4×C22⋊C4D163
hypocenterC163C42×D4
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10432

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 6854);