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2−1+4×C22⋊C9 #11919877

order1152
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C26

Aliases

direct product2−1+4×C22⋊C9

Splittings

SylowC22×2−1+4 ⋊ C9

Subgroups

subgroupG/H
center, FrattiniC2×C3C24×A4
commutatorC23C24×C9
Fitting, prime radicalC22×C3×2−1+4C3
socle, cosocleC23×C3C24×C3
hypercenterC3×2−1+4A4
hypocenterC22C9×2−1+4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C3 ◁ C3×2−1+4

2298 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 2298 conjugacy classes of subgroups — too many to draw. Only its 340 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) = 144

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153888);