Finite Group Databasebeta

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2−1+4×Dic163 #35227749

order20864
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×Dic163

Splittings

SylowC163 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC22C24×D163
commutatorC2×C163C24×C4
Fitting, prime radicalC2×2−1+4×C163C2
socle, cosocleC22×C163C25
hypercenterC2×2−1+4D163
hypocenterC163C4×2−1+4
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×2−1+4

1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10432

Conjugacy classes & character table

2822 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 17723);