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C2×2−1+4×D173 #36368366

order22144
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×D173

Splittings

FittingC2×2−1+4×C173 ⋊ C2
SylowC173 ⋊ C22×2−1+4

Subgroups

subgroupG/H
centerC22C24×D173
commutator, cosocleC2×C173C26
FrattiniC2C25×D173
FittingC2×2−1+4×C173C2
socleC22×C173C25
hypercenterC2×2−1+4D173
hypocenterC173C22×2−1+4
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C2×2−1+4

5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.

normal subgroups only

This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3213 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) = 5536

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 19313);