Finite Group Databasebeta

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Q8×Dic9⋊C4 #11805545

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×Dic9⋊C4

Splittings

SylowC9 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socle, prime radicalC23×C3C23×D3
FittingC2×C4×Q8×C9C2
cosocleC23×C9C24
hypercenterC2×C4×Q8D9
hypocenterC9Q8×C4⋊C4
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×Q8

852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 39556);