Finite Group Databasebeta

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C4×2−1+4⋊C9 #11919689

order1152
automorphism?
homologyAbelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23

Aliases

direct productC4×2−1+4⋊C9
unambiguous semidirect product(C4×2−1+4)⋊C9

Splittings

SylowC4×2−1+4 ⋊ C9

Subgroups

subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C22×C4×C9
Frattini, socleC22×C3C23×A4
FittingC3×C4×2−1+4C3
prime radicalC2×C3×2−1+4C2×C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×C4×D4A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

670 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 145 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) = 576

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153700);