Finite Group Databasebeta

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2−1+4×#10621924 #36370545

order22144
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×#10621924

Splittings

Fitting2−1+4×C173 ⋊ C4
SylowC173 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×#10621924
commutator, socleC2×C173C24×C4
Fitting2−1+4×C173C4
prime radical2−1+4×D173C2
cosocleC2×D173C25
hypercenter2−1+4#10621924
hypocenterC173C4×2−1+4
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ 2−1+4

1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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) = 2768

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 21492);