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C4×#19104720 #35217062

order20864
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19104720

Splittings

FittingC4×C4⋊C4×C163 ⋊ C2
SylowC163 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D163
commutatorC22×C163C23×C4
FrattiniC23C23×D163
FittingC4×C4⋊C4×C163C2
socle, cosocleC23×C163C24
prime radicalC22×D652C22
hypercenterC4×C4⋊C4D163
hypocenterC163C4×#123
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10432

Conjugacy classes & character table

3296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 7036);